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We study the Weyl-type solutions of the differential system with a singularity $y'-x^{-1}Ay-q(x)y=\rho By$ in the case of integrable potential $q(\cdot)$., Comment: arXiv admin note: text overlap with arXiv:1606.01563

A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the alternatives is to assume that one or the other is correct and attempt to draw physical, observable consequences which then could be empirically verified or ruled out. As a working hypothesis, we propose simple models of collapse as a real physical process for direct binary symmetric measurements made on one particle. This allows one to construct irreversible unstable Schr\"odinger equations capable of describing continuously the process of collapse induced by the interaction of the quantum system with the measuring device. Due to unknown initial conditions the collapse outcome remains unpredictable so no contradictions with quantum mechanics arise. Our theoretical framework predicts a finite time-scale of the collapse and links with experiment. Sensitive probes of the collapse dynamics could be done using Bose-Einstein condensates, ultracold neutrons or ultrafast optics. If confirmed, the formulation could be relevant to the transition from quantum fluctuations to classical inhomogeneities in early cosmology and to establishing the ultimate limits on the speed of quantum computation and information processing., Comment: 28 pages, 5 figures, much expanded companion paper to arXiv:1204.3373 [quant-ph]

MOND is one of the most popular alternatives to Dark Matter (DM). While efforts to directly detect DM in laboratories have been steadily pursued over the years, the proposed Earth-based tests of MOND are still in their infancy. Some proposals recently appeared in the literature are briefly reviewed, and it is argued that collaborative efforts of theorists and experimenters are needed to move forward in this exciting new area. Possible future directions are outlined., Comment: 9 pages, Invited paper to appear in the special issue of the Canadian Journal of Physics

Using complex quantum Hamilton-Jacobi formulation, a new kind of non-linear equations is proposed that have almost classical structure and extend the Schroedinger equation to describe the collapse of the wave function as a finite-time process. Experimental bounds on the collapse time are reported (of order 0.1 ms to 0.1 ps) and its convenient dimensionless measure is introduced. This parameter helps to identify the areas where sensitive probes of the possible collapse dynamics can be done. Examples are experiments with Bose-Einstein condensates, ultracold neutrons or ultrafast optics., Comment: 9 pages; v2: a shorter version to suit the 4 page limit of Proceedings of International Conference on Mathematical Modelling in Physical Sciences, 3-7 September 2012, Budapest, Hungary (IC-MSQUARE 2012)

The question if the Bose statistics is broken at the TeV scale is discussed. The decay of a new heavy spin 1 gauge boson Z' into two photons, Z'-> 2 gamma, is forbidden by the Bose statistics among other general principles of quantum field theory (Landau-Yang theorem). We point out that the search for this decay can be effectively used to probe the Bose symmetry violation at the CERN LHC., Comment: 10 pages, 3 figures. Published version, but with extended introductory discussion

The modified-inertia MOND is an approach that proposes a change in Newton's second law at small accelerations as an alternative to dark matter. Recently it was suggested that this approach can be tested in terrestrial laboratory experiments. One way of doing the test is based on the Static High-Latitude Equinox Modified Inertia (SHLEM) effect: around each equinox date, 2 spots emerge on the Earth where static bodies experience spontaneous displacement due to the violation of Newton's second law required by the modified-inertia MOND. Here, a detailed theory of this effect is developed and estimates of the magnitude of the signal due to the effect are obtained. The expected displacement of a mirror in a gravitational wave interferometer is found to be about 10^{-14} m. Some experimental aspects of the proposal are discussed., Comment: 15 pages, 1 figure

Astrophysical observations (usually explained by dark matter) suggest that classical mechanics could break down when the acceleration becomes extremely small (the approach known as modified Newtonian dynamics, or MOND). I present the first analysis of MOND manifestations in terrestrial (rather than astrophysical) settings. A new effect is reported: around each equinox date, 2 spots emerge on the Earth where static bodies experience spontaneous acceleration due to the possible violation of Newton's second law. Preliminary estimates indicate that an experimental search for this effect can be feasible., Comment: 10 pages; minor changes to match the published version

Recently it was suggested that the neutrino may violate the Pauli exclusion Principle (PEP). This renews interest in the systematic search for bilinear commutation relations that could describe deviations from PEP. In the context of this search we prove a no-go theorem which forbids a finite occupancy limit for an arbitrary system with a bilinear commutation relation. In other words, either the upper limit on the occupancy number is 1 (the ordinary fermionic case) or there is no upper limit at all. Some examples of the latter class include the usual Bose statistics, as well as non-standard quon statistics and infinite statistics., Comment: 11 pages, RevTeX4

Since the publication of the models describing a small violation of the Pauli exclusion principle (PEP) there has been an explosion of word-wide interest in PEP tests and related theories. PEP forbids an atom to have more than 2 electrons in the K-shell. If PEP is slightly violated, a third electron can occasionally join in. This would result in an anomalous X-ray emission. A high-sensitivity experiment places an upper limit of the order of 10^{-26} on the PEP violating parameter. I will outline the main theoretical and experimental ideas in this new exciting area., Comment: 12 pages, RevTeX4, Invited talk at the 20th International Conference on X-ray and Inner-shell Processes (Melbourne, Australia, 4-8 July, 2005)

Astrophysical observations suggest that the fine structure constant (alpha) may (or may not) be evolving over the cosmological time scale. This raises a much debated question: is alpha variation due to the variation of the speed of light (c), elementary electric charge (e), or the Planck constant (h)? Previously, we proposed the metrological approach based on the analysis of the relationships between the fundamental units (e.g. of the length and time) and the fundamental constants. Our methodology allows one to find how each of the fundamental constants e, c, h evolves in time and offers a new outlook for this area. Here we give a brief outline of this approach and the main results it produces., Comment: 5 pages, RevTeX4, presented at the 16th National Congress of the Australian Institute of Physics (Canberra, 31 January - 4 February 2005)

We analyse the possible role of new interactions of neutrino in the forthcoming tritium beta decay experiment KATRIN aimed at detecting the neutrino mass with the sensitivity of 0.3 - 0.2 eV. It is shown that under certain circumstances the standard procedure of data analysis would have to be modified by the introduction of an extra parameter describing the strength of the new interactions. Our model simulations show that the modified procedure may improve the quality of the fit compared with the standard case. Ignoring the possibility of new interactions may lead to a systematic error in the neutrino mass determination., Comment: 7 pages, 1 figure, revtex 4; corrected typos, a minor stylistic change in conclusions

We set up a framework for a model-independent analysis of the time variation of $e$, $\hbar$, and $c$ indiviually. It is shown that the time-evolution of each constant can be determined uniquely from the time evolution of the fine structure constant $\alpha$ provided that the choice of basic time-independent units (i.e., the clock and ruler) is fixed. Realistic systems of units are considered as examples and implications for metrology are discussed., Comment: 8 pages, RevTex, revised references and two typos corrected

We report the results of the first computation related to the study of the spectator effects in the rare decay mode $B\to K \gamma \gamma $ within the framework of Standard Model. It is found that the account of these effects results in the enhancement factor for the short-distance reducible contribution to the branching ratio., Comment: 5 pages, 5 figures, RevTeX 4

One of the deepest unsolved puzzles of subatomic physics is why Nature prefers the left particles to the right ones. Mirror matter is an attempt to understand this mystery by assuming the existence of a "parallel''world where this preference is exactly opposite. Thus in the Universe consisting of the ordinary and the mirror matter the symmetry between the left and right is completely restored. Mirror matter is constrained to interact with us only very weakly. Still, its existence can be inferred by using experimental evidence such as the observation of astrophysical objects related to the dark matter (MACHO), neutrino physics and other sources. This talk will focus on several key aspects of mirror matter physics including the possible existence of mirror matter inside the Earth and the suggestion that the recently observed "isolated" planets may in fact be orbiting around mirror stars., Comment: 9 pages, revtex, Talk given by A.Yu.Ignatiev at the 15th Biennual Congress of the Australian Institute of Physics (Sydney, July 2002)

Mirror matter is a dark matter candidate. In this paper, we re-examine the linear regime of density perturbation growth in a universe containing mirror dark matter. Taking adiabatic scale-invariant perturbations as the input, we confirm that the resulting processed power spectrum is richer than for the more familiar cases of cold, warm and hot dark matter. The new features include a maximum at a certain scale $\lambda_{max}$, collisional damping below a smaller characteristic scale $\lambda'_S$, with oscillatory perturbations between the two. These scales are functions of the fundamental parameters of the theory. In particular, they decrease for decreasing $x$, the ratio of the mirror plasma temperature to that of the ordinary. For $x \sim 0.2$, the scale $\lambda_{max}$ becomes galactic. Mirror dark matter therefore leads to bottom-up large scale structure formation, similar to conventional cold dark matter, for $x \stackrel{<}{\sim} 0.2$. Indeed, the smaller the value of $x$, the closer mirror dark matter resembles standard cold dark matter during the linear regime. The differences pertain to scales smaller than $\lambda'_S$ in the linear regime, and generally in the non-linear regime because mirror dark matter is chemically complex and to some extent dissipative. Lyman-$\alpha$ forest data and the early reionisation epoch established by WMAP may hold the key to distinguishing mirror dark matter from WIMP-style cold dark matter., Comment: 17 pages, 4 figures; minor changes, reference added

The physics of kinetic mixing between ordinary and mirror photons is discussed. An important role is played by four linear combinations we dub the physical photon, the sterile photon, the physical mirror photon, and the sterile mirror photon. Because of the mass degeneracy between the two gauge bosons, quantum coherence effects are important. The physical photon becomes a certain coherent superposition of the bare ordinary photon and the bare mirror photon. Similarly, the physical mirror photon is another, but {\it not orthogonal}, coherent superposition. We discuss the physics of the interaction between physical mirror photons and ordinary matter. Observational signatures for some hybrid ordinary/mirror binary astrophysical systems are qualitatively discussed. We show that a small amount of ordinary matter at the center of a mirror star may make the mirror star observable. We speculate that the recently reported halo white dwarfs might actually be mirror halo stars., Comment: RevTeX, 14 pages including 2 figures; Changes to exposition, terminology and referencing; phenomenological conclusions unchanged

We propose that the ``isolated'' planetary mass objects observed by Zapatero Osorio et al in the $\sigma$ Orionis cluster might actually be in orbit around invisible stellar mass companions such as mirror stars. Mirror matter is expected to exist if parity is an unbroken symmetry of nature. Future observations can test this idea by looking for a periodic Doppler shift in the radiation emitted by the planets. The fact that the observations show an inverse dependence between the abundance of the these objects and their mass may argue in favour of the mirror matter hypothesis., Comment: 5 pages, no figures, ReVTeX; altered discussion about observability of the Doppler shifts and other issues

The Mirror Matter or Exact Parity Model sees every standard particle, including the physical neutral Higgs boson, paired with a parity partner. The unbroken parity symmetry forces the mass eigenstate Higgs bosons to be maximal mixtures of the ordinary and mirror Higgs bosons. Each of these mass eigenstates will therefore decay 50% of the time into invisible mirror particles, providing a clear and interesting signature for the Large Hadron Collider (LHC) which could thus establish the existence of the mirror world. However, for this effect to be observable the mass difference between the two eigenstates must be sufficiently large. In this paper, we study cosmological constraints from Big Bang Nucleosynthesis on the mass difference parameter. We find that the temperature of the radiation dominated (RD) phase of the universe should never have exceeded a few 10's of GeV if the mass difference is to be observable at the LHC. Chaotic inflation with very inefficient reheating provides an example of how such a cosmology could arise. We conclude that the LHC could thus discover the mirror world and simultaneously establish an upper bound on the temperature of the RD phase of the universe., Comment: 8pages including 1 figure, RevTeX; minor changes and added references; this version accepted by Phys Lett B

We have performed a detailed investigation of geophysical constraints on the possible admixture of mirror matter inside the Earth. On the basis of the Preliminary Reference Earth Model (PREM) -- the `Standard Model' of the Earth's interior -- we have developed a method which allows one to compute changes in various quantities characterising the Earth (mass, moment of inertia, normal mode frequencies etc.)due to the presence of mirror matter. As a result we have been able to obtain for the first time the direct upper bounds on the possible concentration of the mirror matter in the Earth. In terms of the ratio of the mirror mass to the Earth mass a conservative upper bound is $3.8\times 10^{-3}$. We then analysed possible mechanisms (such as lunar and solar tidal forces, meteorite impacts and earthquakes) of exciting mirror matter oscillations around the Earth centre. Such oscillations could manifest themselves through global variations of the gravitational acceleration at the Earth's surface. We conclude that such variations are too small to be observed. Our results are valid for other types of hypothetical matter coupled to ordinary matter by gravitation only (e.g. the shadow matter of superstring theories)., Comment: 25 pages, in RevTeX, to appear in Phys.Rev.D

We examine the issue of magnetic charge quantization in the presence of black holes. It is pointed out that quantization of magnetic charge can lead to the mass quantization for magnetically charged black holes. We also discuss some implications for the experimental searches of magnetically charged black holes., Comment: RevTeX, 11 pages, Invited paper for the first editorial volume of the book series "Contemporary Fundamental Physics" by the Nova Science Publishers

Hybrid $SU(2) \times U(1)$ models are the models in which $SU(2) \times U(1)$ symmetry is broken down not only spontaneously (as in the Standard Model), but also explicitely by adding a hard mass term for the U(1) field in the lagrangian. We study the issue of electric charge nonconservation and dequantization in these models. For this purpose we construct and analyze a series of hybrid models with different scalar contents. We show that some of these models posess an interesting property: the photon can remain massless (at least, at the tree level) even though the electric charge is not conserved., Comment: 17 pages, revtex

We examine several issues related to the processes of Dirac monopole-antimonopole production in high-energy collisions such as $e^+e^-$ annihilation. Perturbative calculations for such processes are known to be inherently ambiguous due to the arbitrariness of direction of the monopole string; this requires use of some prescription to obtain physical results. We argue that different prescriptions lead to drastically different physical results which suggests that at present we do not have an entirely satisfactory procedure for the elimination of string arbitrariness (this problem is quite separate from the problems caused by the large coupling constant). We then analyze the consequencies of discrete symmetries (P and C) for the monopole production processes and for the monopole-antimonopole states. The P and C selection rules for the monopole-antimonopole states turn out to be different from those for the ordinary fermion-antifermion or boson-antiboson system. In particular, the spin 1/2 monopole and antimonopole should have the same helicities if they are produced through the one-photon annihilation of an electron and positron. A stronger selection rule holds for spinless monopoles: CP symmetry absolutely forbids the monopole-antimonopole production through the one-photon annihilation of an electron and positron. Single-photon $e^+e^- \to g^+g^-$ amplitude has been a key input in calculating the contribution of virtual $g^+g^-$ pairs to various physical processes such as the decay $Z\to 3\gamma$ and the anomalous magnetic moment of the electron. Applying our conclusions to these cases can lead to significant modifications of the results obtained in previous works., Comment: 21 pages, revtex, 5 figures

We address the problem of string arbitrariness in the quantum field theory of Dirac magnetic monopoles. Different prescriptions are shown to yield different physical results. The constraints due to the discrete symmetries (C and P) are derived for the process of electron- positron annihilation into the monopole-antimonopole pair. In the case of the annihilation through the one-photon channel, the production of spin 0 monopoles is absolutely forbidden; spin 1/2 monopole and antimonopole should have the same helicities (or, equivalently, the monopole-antimonopole state should be p-wave $^1P_1$)., Comment: 14 pages, revtex, 3 figures

We study a novel type of extensions of the Standard Model which include a hard mass term for the U(1) gauge field and, optionally, the additional scalar multiplets spontaneously violating the electric charge conservation. Contrary to the case of abelian massive electrodynamics, in these theories the massiveness of photon necessarily implies non-conservation (and also dequantization) of the electric charge (even in the absence of spontaneous breakdown of the electromagnetic symmetry). On the other hand, unexpectedly, there exist models with charge non-conservation where it is possible to keep the photon mass zero (at least, at the tree level)., Comment: 10 pages, revtex, no figures, to appear in Physics Letters B

We investigate in detail the problem of constructing magnetic monopole solutions within the finite-range electrodynamics (i.e., electrodynamics with non-zero photon mass, which is the simplest extension of the standard theory; it is fully compatible with the experiment). We first analyze the classical electrodynamics with the additional terms describing the photon mass and the magnetic charge; then we look for a solution analogous to the Dirac monopole solution. Next, we plug the found solution into the Schr\"{o}dinger equation describing the interaction between the the magnetic charge and the electron. After that, we try to derive the Dirac quantization condition for our case. Since gauge invariance is lost in massive electrodynamics, we use the method of angular momentum algebra. Under rather general assumptions we prove the theorem that the construction of such an algebra is not possible and therefore the quantization condition cannot be derived. This points to the conclusion that the Dirac monopole and the finite photon mass cannot coexist within one and the same theory. Some physical consequences of this conclusion are considered. The case of t'Hooft-Polyakov monopole is touched upon briefly., Comment: 24 pages, revtex, 1 figure appended as a PostScript file

We analyze the role played by the gauge invariance for the existence of Dirac monopole. To this end, we consider the electrodynamics with massive photon and ask if the magnetic charge can be introduced there. We show that the derivation of the Dirac quantization condition based on the angular momentum algebra cannot be generalized to the case of massive electrodynamics. Possible implications of this result are briefly discussed., Comment: 12 pages, revtex, no figures

It has recently been shown that the neutrino can have non-zero electric charge in a number of gauge theories, including the Minimal Standard Model. Assuming non-zero neutrino charge, we develop a new approach to the solar neutrino problem. The key idea is that the charged neutrinos will be deflected by the Lorentz force while they are crossing the solar magnetic fields. Such a deflection will result in the anisotropy of the solar neutrino flux. Because of this anisotropy, the solar neutrino flux registered on earth can be reduced as compared to the Standard Solar Model prediction. The mechanism is purely classical and does not require neutrino oscillations, spin-flip or neutrino decay. We discuss qualitatively the consequences of our scenario for present and future solar neutrino experiments as well as differences between our mechanism and other proposed solutions., Comment: 29 pages, UM-P/94-73, RCHEP-94/21, in REVTEX

We suggest that Bose statistics for photons can be tested by looking for decays of spin-1 bosons into two photons. The experimental upper limit on the decay $Z \rightarrow \gamma \gamma $ is used to establish for the first time the quantitative measure of the validity of Bose symmetry for photons., Comment: 9 pages, in REVTEX, RCHEP-94/17, UM-P-94/63

We have considered the effect of the reduction of the solar neutrino flux on earth due to the deflection of the charged neutrino by the magnetic field of the solar convective zone. The antisymmetry of this magnetic field about the plane of the solar equator induces the anisotropy of the solar neutrino flux thus creating the deficit of the neutrino flux on the earth. The deficit has been estimated in terms of solar and neutrino parameters and the condition of a 50 \% deficit has been obtained: $Q_{\nu} gradH \agt 10^{-18} eG/cm$ where $Q_{\nu}$ is the neutrino electric charge, $gradH$ is the gradient of the solar toroidal magnetic field, e is the electron charge. Some attractive experimental consequences of this scenario are qualitatively discussed., Comment: 15 pages, UM-P/94-26, in REVTEX

We present the limits on possible time variation of the electric charges of quarks and leptons at the time of primordial nucleosynthesis within a model with dequantized electric charges which allows for the case of charged neutrino and neutron., Comment: 9 pages, Physical Review D, in press, in REVTEX, UM-P-93/42