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The Unruh effect, thereby an ideally accelerated quantum detector is predicted to absorb thermalized virtual photons and re-emit real photons, is significantly extended for laboratory accessible configurations. Using modern influence functional techniques, we obtain explicit expressions describing the excitation and relaxation of the quantum levels of an Unruh detector as a general noninertial open quantum system. Remarkably, for controllable periodical motions, an exact master equation is found for the Unruh detector within the prevailing framework of quantum optics with a well-defined Unruh temperature for given acceleration ($\alpha$), acceleration frequency ($\omega_\alpha$), and transition frequency ($\omega_0$) of the detector. We further show that the measurable Unruh temperatures and corresponding transition rates are comparable or higher than their values for the ideally accelerated cases if $c\omega_0$ and $c\omega_\alpha$ have similar orders of magnitude as $\alpha$. This allows us to select the transition rates of the detector to unmask Unruh radiation against Larmor radiation which has been a major competing noise. Our work suggests experiments with such settings may directly confirm the Unruh effect within the current technology, based on which a laboratory test of black hole thermodynamics will become possible., Comment: 6 pages, 3 figures

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves., Comment: 16 pages, 3 figures, version published in the Special Issue of Symmetry "New Frontiers in Quantum Gravity"

We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal class of Ashtekar-Barbero connection variables is constructed, which can be quantized using spin networks. Crucially, the quantum states become separable into the eigen states of the generator of the scale transformation and spin-network states in the Einstein frame. The eigen values consist of additional quantum numbers including a new type of fundamental frequency $\omega$ and energy $E = \hbar \omega$ with respect to a new local time $\tau$ carried by every spin-network vertex. The discretely distributed $\tau$ values as the "quanta of time" correspond to a functional time related to the integrated Weyl current in the classical theory. The Immirzi ambiguity of loop quantum geometry is removed by scale symmetry. To probe the quantum behaviour of the early Universe, the new formalism is applied to a scale-invariant homogenous and isotropic cosmological model coupled to a doublet of scalars with illustrative numerical simulations. The Einstein-frame volume is quantized in recently improved and regularized polymer representations with an arbitrary Immirzi parameter. The resulting unitary evolution of the quantum state of an expanding universe has a positive energy spectrum. A rescaling of the Immirzi parameter is equivalent to a translation in time without changing dynamics. The big bang can be identified in the past time limit when the expectation values of the Jordan-frame volume tend to zero. Remarkably, the quantized big bang is not replaced by a big bounce---a prevalent scenario in present loop quantum cosmology., Comment: 7 pages, 4 figures, version to appear in PLB

This article is an extended version of the peer-reviewed publication; Moffat and Wang, J Phys Math 2018, 9:4 DOI: 10.4172/2090-0902.1000289 The article sets out to address a number of issues concerning Loop Quantum Gravity raised by Ashtekar, such as in a recent post to Arxiv.org (A Ashtekar Arxiv:gr-qc /0702030 v 2.0 May 2007). These include, for example, conditions for the existence of Poincare invariant quantum states. In doing so, this article provides a coherent mathematical framework for both the evolution of space-time and the supersymmetric graviton in the early universe. In this extended form, it is mnhopefully more accessible to research students at the advanced undergraduate level and beginning doctoral level. The key extensions are: a. An explicit cohomology based link between movement across a computational spin network and a dimensioned embedding of the network to produce equivalent movement along a discrete path in space-time; b). A discussion of the implications for quantum ergodic theory and black hole dynamics., Comment: The previous version (v1) remains. Version 2 now appears as arXiv:1612.01018v2

A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general relativity and scale-invariant scalar-tensor and dilaton theories. Consequently, matter to be coupled to such theories is restricted to be conformal or scale invariant. Standard model-type systems naturally fall into this category. The new loop quantization follows from a novel conformally generalized Holst action principle. In contrast to standard loop quantum gravity, the resulting quantum geometry is not beset by the Immirzi ambiguity and has no definitive area gaps within the considered large class of theories of gravitation. As an additional feature, the scale invariance gives rise to a conserved Weyl current and we discuss briefly its possible implication on the problem of time in quantum gravity., Comment: 35 pages (8 pages main text, 27 pages supplementary material); Published version

Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. Here, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. In particular, we introduce a conformal Einstein frame in which loop quantization is implemented. We then discuss how different Immirzi parameters under this description may be related by conformal frame transformations and yet share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field., Comment: 11 pages, proofread version to be published by Physical Review D

We consider the nonunitary quantum dynamics of neutral massless scalar particles used to model photons around a massive gravitational lens. The gravitational interaction between the lensing mass and asymptotically free particles is described by their second-quantized scattering wavefunctions. Remarkably, the zero-point spacetime fluctuations can induce significant decoherence of the scattered states with spontaneous emission of gravitons, thereby reducing the particles' coherence as well as energy. This new effect suggests that, when photon polarizations are negligible, such quantum gravity phenomena could lead to measurable anomalous redshift of recently studied astrophysical lasers through a gravitational lens in the range of black holes and galaxy clusters., Comment: 4 pages, 2 figures, references updated

We carry out a theoretical investigation on the collective dynamics of an ensemble of correlated atoms, subject to both vacuum fluctuations of spacetime and stochastic gravitational waves. A general approach is taken with the derivation of a quantum master equation capable of describing arbitrary confined nonrelativistic matter systems in an open quantum gravitational environment. It enables us to relate the spectral function for gravitational waves and the distribution function for quantum gravitational fluctuations and to indeed introduce a new spectral function for the zero-point fluctuations of spacetime. The formulation is applied to two-level identical bosonic atoms in an off-resonant high-$Q$ cavity that effectively inhibits undesirable electromagnetic delays, leading to a gravitational transition mechanism through certain quadrupole moment operators. The overall relaxation rate before reaching equilibrium is found to generally scale collectively with the number $N$ of atoms. However, we are also able to identify certain states of which the decay and excitation rates with stochastic gravitational waves and vacuum spacetime fluctuations amplify more significantly with a factor of $N^2$. Using such favourable states as a means of measuring both conventional stochastic gravitational waves and novel zero-point spacetime fluctuations, we determine the theoretical lower bounds for the respective spectral functions. Finally, we discuss the implications of our findings on future observations of gravitational waves of a wider spectral window than currently accessible. Especially, the possible sensing of the zero-point fluctuations of spacetime could provide an opportunity to generate initial evidence and further guidance of quantum gravity., Comment: 14 pages, 4 figures, with typo corrections

We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A systematic approach to the generation of gravitational waves in the quantum domain is presented that recovers known classical limits in terms of the quadrupole radiation formula and backreaction dissipation. Classical gravitational emission and absorption relations are quantized into their quantum field theoretical counterparts in terms of the corresponding operators and quantum ensemble averages. Certain arising consistency issues related to factor ordering have been addressed and resolved. Using the theoretical formulation established here with numerical simulations in the quantum regime, we discuss potential new effects including decoherence through the spontaneous emission of gravitons and collectively amplified radiation of gravitational waves by correlated quantum particles., Comment: 17 pages, 3 figures, proofread version to be published by Physical Review D

We develop further our fibre bundle construct of non-commutative space-time on a Minkowski base space. We assume space-time is non-commutative due to the existence of additional non-commutative algebraic structure at each point x of space-time, forming a quantum operator 'fibre algebra' A(x). This structure then corresponds to the single fibre of a fibre bundle. A gauge group acts on each fibre algebra locally, while a 'section' through this bundle is then a quantum field of the form {A(x); x in M} with M the underlying space-time manifold. In addition, we assume a local algebra O(D) corresponding to the algebra of sections of such a principal fibre bundle with base space a finite and bounded subset of space-time, D. The algebraic operations of addition and multiplication are assumed defined fibrewise for this algebra of sections. We characterise 'ergodic' extremal quantum states of the fibre algebra invariant under the subgroup T of local translations of space-time of the Poincare group P in terms of a non-commutative extension of entropy applied to the subgroup T. We also characterise the existence of T- invariant states by generalizing to the non-commutative case Kakutani's work on wandering projections. This leads on to a classification of the structure of the local algebra O(D) by using a 'T-Twisted' equivalence relation, including a full analysis of the T-type III case. In particular we show that O(D) is T-type III if and only if the crossed product algebra O(D)xT is type III in the sense of Murray-von Neumann., Comment: 16 pages

With recent developments in high-precision quantum measurements, the question of whether observations of decoherence from spacetime fluctuations are accessible experimentally arises. Here we investigate the dynamics of bound states interacting with an environment of gravitons under the Markov approximation. The corresponding Lindblad master equation is presented that enables gravitational decoherence and dissipation due to zero-point spacetime fluctuations to be analyzed. Specifically, we consider a one-dimensional cavity of massless scalar particles that models a light beam with negligible spin polarizations being reflected between two free masses. Numerical simulations have been performed to illustrate the wave-modal dependent decoherence and dissipation of such a configuration. We further demonstrate the existence of nontrivial collective effects akin to superradiance, providing amplifications of gravitational decoherence for a large number of identical bosonic particles., Comment: 9 pages; Submitted for the IARD 2016 Proceedings

We develop a new mathematical approach to diffeomorphism invariant quantum states for the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators acting on the fibre algebra that defines a Hilbert space. The algebras of two types of operators are considered in detail, namely the observables as generic physical variables and the quantum operators suitable for describing symmetries and transformations. We then introduce generalised quantum states of these operators and examine their properties. By establishing a link between the commutativity and group cohomology of the translational group as a subgroup of the Poincare group, we show that this leads to the construction of quantum states invariant under the action of the translational group, as the local gauge group of diffeomorphisms, with unitary representations., Comment: 14 pages; updated with clarifications and references

The influence of spacetime foam on a broad class of bosonic fields with arbitrary numbers of particles in the low energy regime is investigated. Based on recently formulated general description of open quantum gravitational systems, we analyse the propagation of scalar, electromagnetic, and gravitational waves on both long and short time scales with respect to their mean frequencies. For the long time propagation, the Markov approximation is employed that neglects the effects of initial conditions of these waves. In this case, despite intuitively expected decoherence and dissipation from the noisy spacetime, we show that such phenomena turn out to be completely suppressed for scalar bosons, photons, and gravitons, which are coupled to gravity but otherwise free. The short time effects are then recovered through the transient non-Markovian evolution. Focusing on scalar bosons in initially incoherent states, we find that the resulting quantum dissipation depend strongly on the distribution of the particle momentum states. We further identify a hitherto undiscovered collective anti-dissipation mechanism for a large number of particles. The surprising new effect tends to "bundle" identical particles within a sharply distributed momentum states having a width inversely proportional to the particle number due to the thermal fluctuations, or its square root due to the vacuum fluctuations of spacetime., Comment: 7 pages; typos corrected

Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms of energy and matter causing decoherence. This may have subtle implications on precision laboratory experiments and astronomical observations and could limit the ultimate capacities for quantum technologies prone to decoherence. To establish the essential physical mechanism of decoherence under weak spacetime fluctuations, we carry out a sequence of analytical steps utilizing the Dirac constraint quantization and gauge invariant influence functional techniques, resulting in a general master equation of a compact form, that describes an open quantum gravitational system with arbitrary bosonic fields. An initial application of the theory is illustrated by the implied quantum gravitational dissipation of light as well as (non)relativistic massive or massless scalar particles. Related effects could eventually lead to important physical consequences including those on a cosmological scale and for a large number of correlated particles., Comment: 7 pages; final version

The Witten-Yau theorem in the AdS/CFT correspondence conjectures that the conformal boundary to AdS space must possess a metric of non-negative scalar curvature for the conformal field theory defined thereon to be free of pathologies. By employing various tools from conformal geometry - such as almost Einstein structures, collapsing sphere products and tractor bundles - we rigorously prove this conjecture., Comment: It has come to our attention that theorem .5 has been misapplied, thereby invalidating the result

We consider the gravitational stability of a current carrying filamentary cloud in the presence of both axial and azimuthal magnetic fields using a simple analytic model. The azimuthal magnetic field is shown to give rise to a new contribution, dictated by Ampere's law, in the corresponding virial equation for magnetohydrodynamic equilibrium. From this we obtain a computationally inexpensive guidance on the gravitational stability of current carrying filamentary clouds. The approach not only provides a fresh insight into the essential physical mechanisms involved, but also demonstrates clearly that, for sufficiently large and yet astronomically realistic currents, the azimuthal magnetic field can cause filamentary clouds to undergo instability., Comment: 7 pages, 2 column aastex, to appear in ApJ

The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichm\"{u}ller space of conformal structures on a Riemann surface. In this article we show that the configuration space of conformal connection-dynamics is naturally a higher-dimensional Teichm\"{u}ller space, subject to the same condition. An immediate consequence of this result is that the Barbero-Immirzi parameter of loop quantum gravity naturally assumes a dilatonic character in all conformal canonical gravity theories.

We investigate the position oscillation of a particle that models the center of mass quantum state of a trapped Bose-Einstein condensate coupled to the zero-point fluctuations of the gravitational field. A semiclassical analysis is performed that allows to calculate the mean square amplitude of the oscillation. In analogy with the Lamb shift in quantum electrodynamics, this gives rise to an upshift of the energy of the trapped condensates. We show that for an elongated trap, the energy shift scales quadratically with the length as well as cubically with the total number of atoms., Comment: 8 pages; published version

We identify a new dynamical mechanism for a strong scalar gravitational field effect. To illustrate this mechanism, we investigate the parametric excitation and emission of scalar gravitational waves by a radially pulsating model neutron star., Comment: 4 pages, published version

We investigate the dephasing suffered by a nonrelativistic quantum particle within a conformally fluctuating spacetime geometry. Starting from a minimally coupled massive Klein-Gordon field, the low velocity limit yields an effective Schrodinger equation where the wave function couples to gravity through an effective nonlinear potential induced by the conformal fluctuations. The quantum evolution is studied through a Dyson expansion scheme up to second order. We show that only the nonlinear part of the potential can induce dephasing. This happens through an exponential decay of the off diagonal terms of the particle density matrix. The bath of conformal radiation is modeled in 3-dimensions and its statistical properties are described in general in terms of a power spectral density. The case of a Lorentz invariant spectral density, allowing to model vacuum fluctuations at a low energy domain, is investigated and a general formula describing the loss of coherence derived. This depends quadratically on the particle mass and on the inverse cube of a typical particle dependent cutoff scale. Finally, the possibilities for experimental verification are discussed. It is shown that current interferometry experiments cannot detect such an effect. However this conclusion may improve by using high mass entangled quantum states., Comment: 30 pages, 4 figures; to appear in Class. Quantum Grav. (2009)

We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical approach to the quantum fluctuations of spacetime is developed. The work extends conceptually Boyer's random electrodynamics to a theory of random gravity but has a considerably richer structure for inheriting nonlinearity from general relativity. Attention is drawn to subtleties in choosing boundary conditions for metric fluctuations in relation to their dynamical consequences. Those compatible with the observed Lorentz invariance must allow for spontaneous conformal fluctuations, in addition to stochastic gravitational waves due to zero point gravitons. This is implemented through an effective metric defined in terms of the random spacetime metric modulo a fluctuating conformal factor. It satisfies an effective Einstein equation coupled to an effective stress-energy tensor incorporating gravitational self energy of metric fluctuations as well as matter fields. The effective Einstein equation is expanded up to second order nonlinearity. A UV-cutoff is introduced whose specific value, however, does not enter into the resulting description of random gravity. The averaged effective metric satisfies the empty space Einstein equation with an effective cosmological constant. This vanishes when only the massless matter fields are included. More generally, a finite effective cosmological constant compatible with the observational constraints can be obtained as long as the bare masses of the massive matter fields are nearly zero, or the conformal invariance of matter is restored at some high energy scale., Comment: 19 pages, two-column revtex4 format

The emergence of loop quantum gravity over the past two decades has stimulated a great resurgence of interest in unifying general relativity and quantum mechanics. Amongst a number of appealing features of this approach are the intuitive picture of quantum geometry using spin networks and powerful mathematical tools from gauge field theory. However, the present form of loop quantum gravity suffers from a quantum ambiguity, due to the presence of a free (Barbero-Immirzi) parameter. Following recent progress on the conformal decomposition of gravitational fields, we present a new phase space for general relativity. In addition to spin-gauge symmetry, the new phase space also incorporates conformal symmetry making the description parameter free. The Barbero-Immirzi ambiguity is shown to occur only if the conformal symmetry is gauge-fixed prior to quantization. By withholding its full symmetries, the new phase space offers a promising platform for the future development of loop quantum gravity. This paper aims to provide an exposition, at a reduced technical level, of the above theoretical advances and their background developments. Further details are referred to cited references., Comment: 17 pages, 6 figures, To appear in the 2006 Christmas Issue of Phil. Trans. Roy. Soc. A

One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show that the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future., Comment: 8 pages; final version to appear in CQG as a letter

The newly found conformal decomposition in canonical general relativity is applied to drastically simplify the recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many of the main structures of the existing canonical framework for loop quantum gravity related to the spin network and Thiemann's regularization. However, the Barbero-Immirzi parameter is now converted into the conformal factor as a canonical variable. It behaves like a scalar field but is somehow non-dynamical since the effective Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed., Comment: 10 pages

A new canonical transformation is found that enables the direct canonical treatment of the conformal factor in general relativity. The resulting formulation significantly simplifies the previously presented conformal geometrodynamics. It provides a further theoretical basis for the conformal approach to loop quantum gravity and offers a generic framework for the conformal analysis of spacetime dynamics., Comment: 6 pages

A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric and the triad levels. At the metric level, it is shown that by extending the Arnowitt-Deser-Misner (ADM) phase space of general relativity (GR), a conformal form of geometrodynamics can be constructed. In addition to the Hamiltonian and diffeomorphism constraints, an extra first class constraint is introduced to generate conformal transformations. This phase space consists of York's mean extrinsic curvature time, conformal three-metric and their momenta. At the triad level, the phase space of GR is further enlarged by incorporating spin-gauge as well as conformal symmetries. This leads to a canonical formulation of GR using a new set of real spin connection variables. The resulting gravitational constraints are first class, consisting of the Hamiltonian constraint and the canonical generators for spin-gauge and conformorphism transformations. The formulation has a remarkable feature of being parameter-free. Indeed, it is shown that a conformal parameter of the Barbero-Immirzi type can be absorbed by the conformal symmetry of the extended phase space. This gives rise to an alternative approach to loop quantum gravity that addresses both the conceptual problem of time and the technical problem of functional calculus in quantum gravity., Comment: 6 pages, 1 figure, LaTeX with jpconf.cls and jpconf11.clo, Talk given at Constrained Dynamics and Quantum Gravity 05, Cala Gonone, Sardinia, Italy, 12-16 September 2005

We present a parameter-free gauge formulation of general relativity in terms of a new set of real spin connection variables. The theory is constructed by extending the phase space of the recently formulated conformal geometrodynamics for canonical gravity to accommodate a spin gauge description. This leads to a further enlarged set of first class gravitational constraints consisting of a reduced Hamiltonian constraint and the canonical generators for spin gauge and conformorphism transformations. Owing to the incorporated conformal symmetry, the new theory is shown to be free from an ambiguity of the Barbero-Immirzi type., Comment: 4 pages; minor clarifications made; new refs added

We present a new approach to the Sachs-Wolfe effect, which is based on the dynamics of photons in a space and time varying gravitational field. We consider the influence of plasma dispersion effects on photon propagation, and establish the limits of validity of the usual results of the standard cosmological approach, for the large scale temperature anisotropies of the cosmic microwave background. New dynamical contributions to the integrated Sachs-Wolfe effect are also discussed., Comment: 5 pages

The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the ADM phase space for canonical general relativity to that consisting of York's mean exterior curvature time, conformal three-metric and their momenta. Accordingly, an additional constraint is introduced, called the conformal constraint. In terms of the new canonical variables, a diffeomorphism constraint is derived from the original momentum constraint. The Hamiltonian constraint then takes a new form. It turns out to be the sum of an expression that previously appeared in the literature and extra terms quadratic in the conformal constraint. The complete set of the conformal, diffeomorphism and Hamiltonian constraints are shown to be of first class through the explicit construction of their Poisson brackets. The extended algebra of constraints has as subalgebras the Dirac algebra for the deformations and Lie algebra for the conformorphism transformations of the spatial hypersurface. This is followed by a discussion of potential implications of the presented theory on the Dirac constraint quantization of general relativity. An argument is made to support the use of the York time in formulating the unitary functional evolution of quantum gravity. Finally, the prospect of future work is briefly outlined., Comment: 8 pages, REVTeX, Final version with improved presentation to appear in PRD

In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the exact nonlinear kinematic relationships in the sense of Cosserat theory, and adopt the Bernoulli hypothesis. For the sake of simplicity, the Kirchoff constitutive relations are adopted to provide an adequate description of elastic properties in terms of a few elastic moduli. A deformed configuration of the rod is described by the displacement vector of the deformed centroid curves and an orthonormal moving frame, rigidly attached to the cross-section of the rod. The position of the moving frame relative to the inertial frame is specified by the rotation matrix, parametrized by a rotational vector. The approximate solutions of the nonlinear partial differential equations of motion in quasi-static sense are chosen as the shape functions with up to third order nonlinear terms of generic nodal displacements. Based on the Lagrangian constructed by the Cosserat kinetic energy and strain energy expressions, the principle of virtual work is employed to derive the ordinary differential equations of motion with third order nonlinear generic nodal displacements. A simple example is presented to illustrate the use of the formulation developed here to obtain the lower order nonlinear ordinary differential equations of motion of a given structure. The corresponding nonlinear dynamical responses of the structures have been presented through numerical simulations by Matlab software., Comment: Submitted paper, 31 pages

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analyzed as nonlinear quantum minisuperspaces in the context of the proposed theory., Comment: 14 pages. Classical and Quantum Gravity (To appear)

By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to nonlinear quantum mechanics. This generalization enables a unitary description of the quantum evolution for a broad class of constrained Hamiltonian systems with a nonlinear kinematic structure. In particular, the new theory is applicable to the quantization of cosmological models where a chosen gravitational degree of freedom acts as geometric time. This is demonstrated explicitly using three cosmological models: the Friedmann universe with a massless scalar field and Bianchi type I and IX models. Based on these investigations, the prospect of further developing the proposed quantization scheme in the context of quantum gravity is discussed., Comment: 14 pages