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A systematic investigation of the average multiplicities of light charged particles and intermediate mass fragments emitted in peripheral and semiperipheral collisions is presented as a function of the beam energy, violence of the collision and mass of the system. The data have been collected with the "Fiasco" setup in the reactions 93Nb+93Nb at 17, 23, 30, 38AMeV and 116Sn+116Sn at 30, 38AMeV. The midvelocity emission has been separated from the emission of the projectile-like fragment. This last component appears to be compatible with an evaporation from an equilibrated source at normal density, as described by the statistical code Gemini at the appropriate excitation energy. On the contrary, the midvelocity emission presents remarkable differences for what concerns both the dependence of the multiplicities on the energy deposited in the midvelocity region and the isotopic composition of the emitted light charged particles., Comment: 18 pages, 17 figures, Revtex 4

Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular classical field theory. In particular, their Lagrangians and Hamiltonians must satisfy rather restrictive Noether identities. For instance, this is the case of relativistic mechanics and classical string theory., Comment: 19 pages

Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian completely integrable Hamiltonian system., Comment: 11 pages, accepted for publication in Phys. Lett. A

The processes of coherent bremsstrahlung (CB) and coherent pair production (CPP) based on aligned crystal targets have been studied in the energy range 20-170 GeV. The experimental arrangement allowed for measurements of single photon properties of these phenomena including their polarization dependences. This is significant as the theoretical description of CB and CPP is an area of active theoretical debate and development. With the theoretical approach used in this paper both the measured cross sections and polarization observables are predicted very well. This indicates a proper understanding of CB and CPP up to energies of 170 GeV. Birefringence in CPP on aligned crystals is applied to determine the polarization parameters in our measurements. New technologies for high energy photon beam optics including phase plates and polarimeters for linear and circular polarization are demonstrated in this experiment. Coherent bremsstrahlung for the strings-on-strings (SOS) orientation yields a larger enhancement for hard photons than CB for the channeling orientations of the crystal. Our measurements and our calculations indicate low photon polarizations for the high energy SOS photons., Comment: 23 pages, 27 figures, 2 tables, REVTeX4 two columns

We address the problem of extending an original field Lagrangian to ghosts and antifields in order to satisfy the master equation in the framework of the BV quantization of Lagrangian field systems. This extension essentially depends on the degeneracy of an original Lagrangian whose Euler-Lagrange operator generally obeys the Noether identities which need not be independent, but satisfy the first-stage Noether identities, and so on. A generic Lagrangian system of even and odd fields on an arbitrary smooth manifold is examined in the algebraic terms of the Grassmann-graded variational bicomplex. We state the necessary and sufficient condition for the existence of the exact antifield Koszul-tate complex whose boundary operator provides all the Noether and higher-stage Noether identities of an original Lagrangian system. The Noether inverse second theorem that we prove associates to this Koszul-Tate complex the sequence of ghosts whose ascent operator provides the gauge and higher-stage gauge supersymmetries of an original Lagrangian. We show that an original Lagrangian is extended to a solution of the master equation if this ascent operator admits a nilpotent extension and only if it is extended to an operator nilpotent on the shell., Comment: 32 pages

The CERN-NA-59 experiment examined a wide range of electromagnetic processes for multi-GeV electrons and photons interacting with oriented single crystals. The various types of crystals and their orientations were used for producing photon beams and for converting and measuring their polarisation. The radiation emitted by 178 GeV unpolarised electrons incident on a 1.5 cm thick Si crystal oriented in the Coherent Bremsstrahlung (CB) and the String-of-Strings (SOS) modes was used to obtain multi-GeV linearly polarised photon beams. A new crystal polarimetry technique was established for measuring the linear polarisation of the photon beam. The polarimeter is based on the dependence of the Coherent Pair Production (CPP) cross section in oriented single crystals on the direction of the photon polarisation with respect to the crystal plane. Both a 1 mm thick single crystal of Germanium and a 4 mm thick multi-tile set of synthetic Diamond crystals were used as analyzers of the linear polarisation. A birefringence phenomenon, the conversion of the linear polarisation of the photon beam into circular polarisation, was observed. This was achieved by letting the linearly polarised photon beam pass through a 10 cm thick Silicon single crystal that acted as a "quarter wave plate" (QWP) as suggested by N. Cabibbo et al., Comment: Presented at International workshop "Relativistic Channeling and Related Coherent Phenomena", Frascati (Rome) 23-26 March 2004

A generic degenerate Lagrangian system of even and odd fields is examined in algebraic terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. We show that, if a certain necessary and sufficient condition holds, one can associate to a degenerate Lagrangian system the exact Koszul-Tate complex with the boundary operator whose nilpotency condition restarts all its Noether and higher-stage Noether identities. This complex provides a sufficient analysis of the degeneracy of a Lagrangian system for the purpose of its BV quantization., Comment: 23 pages

We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles over X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved., Comment: 31 pages, to be published in J. Math. Phys

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge symmetries and Noether's identities are formulated, and their equivalence by means of certain intertwining operator is proved., Comment: 20 pages, to be published in J. Phys. A (2005)

Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory., Comment: the invited plenary lecture deliverd at 9th International Conference on Differential Geometry and its Applications, Prague, 2004

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The present book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization., Comment: Preface, Contents and Bibliography, 26 pages

Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational formula and conservation laws for Lagrangian systems on graded manifolds using contact supersymmetries are obtained., Comment: 28 pp., appears in 'Communications in Mathematical Physics'

We present new results regarding the features of high energy photon emission by an electron beam of 178 GeV penetrating a 1.5 cm thick single Si crystal aligned at the Strings-Of-Strings (SOS) orientation. This concerns a special case of coherent bremsstrahlung where the electron interacts with the strong fields of successive atomic strings in a plane and for which the largest enhancement of the highest energy photons is expected. The polarization of the resulting photon beam was measured by the asymmetry of electron-positron pair production in an aligned diamond crystal analyzer. By the selection of a single pair the energy and the polarization of individual photons could be measured in an the environment of multiple photons produced in the radiator crystal. Photons in the high energy region show less than 20% linear polarization at the 90% confidence level., Comment: 8 pages, 7 figures, REVTeX4 two column, Version for publication

Peripheral and semi-peripheral collisions have been studied in the system 93Nb+93Nb at 38 AMeV. The evaporative and midvelocity components of the light charged particle and intermediate mass fragment emissions have been carefully disentangled. In this way it was possible to obtain the average amount not only of charge and mass, but also of energy, pertaining to the midvelocity emission, as a function of an impact parameter estimator. This emission has a very important role in the overall balance of the reaction, as it accounts for a large fraction of the emitted mass and for more than half of the dissipated energy. As such, it may give precious clues on the microscopic mechanism of energy transport from the interaction zone toward the target and projectile remnants., Comment: 4 pages, 3 figures, RevTex4 style

Though a global Chern-Simons (2k-1)-form is not gauge invariant, this form seen as a Lagrangian of higher-dimensional gauge theory leads to the conservation law of a modified Noether current., Comment: 8 pages, appear in Modern Physics Letters A

We present the first experimental results on the use of a thick aligned Si crystal acting as a quarter wave plate to induce a degree of circular polarisation in a high energy linearly polarised photon beam. The linearly polarised photon beam is produced from coherent bremsstrahlung radiation by 178 GeV unpolarised electrons incident on an aligned Si crystal, acting as a radiator. The linear polarisation of the photon beam is characterised by measuring the asymmetry in electron-positron pair production in a Ge crystal, for different crystal orientations. The Ge crystal therefore acts as an analyser. The birefringence phenomenon, which converts the linear polarisation to circular polarisation, is observed by letting the linearly polarised photons beam pass through a thick Si quarter wave plate crystal, and then measuring the asymmetry in electron-positron pair production again for a selection of relative angles between the crystallographic planes of the radiator, analyser and quarter wave plate. The systematics of the difference between the measured asymmetries with and without the quarter wave plate are predicted by theory to reveal an evolution in the Stokes parameters from which the appearance of a circularly polarised component in the photon beam can be demonstrated. The measured magnitude of the circularly polarised component was consistent with the theoretical predictions, and therefore is in indication of the existence of the birefringence effect., Comment: 12 pages, 12 figures, 1 table, REVTeX4 two column, Version for publication

The cross section for coherent pair production by linearly polarised photons in the 20-170 GeV energy range was measured for photon aligned incidence on ultra-high quality diamond and germanium crystals. The theoretical description of coherent bremsstrahlung and coherent pair production phenomena is an area of active theoretical debate and development. However, under our experimental conditions, the theory predicted the combined cross section and polarisation experimental observables very well indeed. In macroscopic terms, our experiment measured a birefringence effect in pair production in a crystal. This study of this effect also constituted a measurement of the energy dependent linear polarisation of photons produced by coherent bremsstrahlung in aligned crystals. New technologies for manipulating high energy photon beams can be realised based on an improved understanding of QED phenomena at these energies. In particular, this experiment demonstrates an efficient new polarimetry technique. The pair production measurements were done using two independent methods simultaneously. The more complex method using a magnet spectrometer showed that the simpler method using a multiplicity detector was also viable., Comment: 10 pages, 13 figures, 1 table, REVTeX4 two column, Version for publication

Generalized symmetries and supersymmetries depending on derivatives of dynamic variables are treated in a most general setting. Studding cohomology of the variational bicomplex, we state the first variational formula and conservation laws for Lagrangian systems on fiber bundles and graded manifolds under generalized symmetries and supersymmetries of any order. Cohomology of nilpotent generalized supersymmetries are obtained., Comment: 29 pages

Motivated by BRST theory, we study generalized symmetries and supersymmetries depending on derivatives of dynamic variables in a most general setting. We state the first variational formula and conservation laws for higher order Lagrangian systems on fiber bundles and graded manifolds under generalized symmetries and supersymmetries of any order. Cohomology of nilpotent generalized supersymmetries are considered., Comment: 17 pages

Given a finite order Lagrangian L on a fibre bundle, its global generalized symmetries depending on higher order derivatives of dynamic variables are considered. The first variational formula is obtained. It leads both to the corresponding Lagarngian conservation laws and the characteristic equation for generalized symmetries of L., Comment: 8 pages

Given a completely integrable system, we associate to any connection on its invariant tori fibred over a parameter manifold the classical and quantum holonomy operator (generalized Berry's phase factor), without any adiabatic approximation., Comment: 15 pages

The applications of Resistive Plate Chambers (RPCs) have recently been extended by the development of counters with time resolution below 100 ps sigma for minimum ionising particles. Applications to HEP experiments have already taken place and many further applications are under study. In this work we address the operating principles of such counters along with some present challenges, with emphasis on counter aging., Comment: Presented at "PSD6 - 6th International Conference on Position Sensitive Detectors", 9-13 September 2002, Leicester, UK. Submitted to Nuclear Instruments and Methods A

Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact) invariant manifold which makes this dynamical system into a partially integrable Hamiltonian system. This Poisson structure is by no means unique. Bi-Hamiltonian partially integrable systems are described in some detail. As an outcome, we state the conditions of quasi-periodic stability (the KAM theorem) for partially integrable Hamiltonian systems., Comment: 18 pages

We provide a symplectic reduction of a partially integrable Hamiltonian system to a completely integrable one. The KAM theorem is applied to this reduced completely integrable Hamiltonian system. Its KAM perturbation generates a perturbation of the original partially integrable system such that the set of tori kept by this perturbation is large., Comment: 6 pages

The $\phi$-meson production cross section is measured for the first time at a sub-threshold energy of 1.93 AGeV in \nuc{58}{Ni}+\nuc{58}{Ni} central collisions. The $\phi$ data were obtained within the acceptance of the CDC/Barrel subsystem of FOPI. For a sample of $4.7\cdot 10^6$ central events, after background subtraction, 23 candidates were observed. Extensive GEANT simulations of the detector performance are shown in a thorough comparison to the real response, aiming at a good understanding of the apparatus and at a trustable determination of the efficiencies, production probability and possible systematic errors. A filter procedure is elaborated, which is meant to facilitate the comparison of any theoretical calculation or new data with the current ones. How to extrapolate the present value to a $\phi$-meson cross section in $4\pi$ is also discussed. This result on pseudo-vector mesons can now be compared to existing experimental knowledge for the same reaction at the same incident energy for various outgoing channels, $K^+$ and $K^-$ included. A significant fraction (at least 20%) of the $K^-$-mesons is originating in the decay of the $\phi$, supporting the statement that the two channels are strongly correlated., Comment: 48 pages, 10 figures submitted to Nucl.-Phys. A Minor wording corrections, a small inconsistency has been corrected in sect.3.3

Completely integrable Hamiltonian systems look promising for controllability since their first integrals are stable under an internal evolution, and one may hope to find a perturbation of a Hamiltonian which drives the first integrals at will. Action-angle coordinates are most convenient for this purpose. Written with respect to these coordinates, a Hamiltonian and first integrals depend only on the action ones. We introduce a suitable perturbation of a Hamiltonian by a term containing time-dependent parameters so that an evolution of action variables is nothing else than a displacement along a curve in a parameter space. Therefore, one can define this evolution in full by an appropriate choice of parameter functions. Similar holonomy controllability of finite level quantum systems is of special interes in connection with quantum computation. We provide geometric quantization of a time-dependent completely integrable Hamiltonian system in action-angle variables. Its Hamiltonian and first integrals have time-independent countable spectra. The holonomy control operator in this countable level quantum system is constructed., Comment: 17 pages

We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom also make up a completely integrable system. They provide m additional first integrals which characterize a relative motion., Comment: 6 pages

A time-dependent completely integrable Hamiltonian system is proved to admit the action-angle coordinates around any regular instantly compact invariant manifold. Written relative to these coordinates, its Hamiltonian and first integrals are functions only of action coordinates., Comment: 9 pages

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The associated quantum algebra consists of functions affine in action coordinates. We obtain a set of its nonequivalent representations in the separable pre-Hilbert space of smooth complex functions on the torus where action operators and a Hamiltonian are diagonal and have countable spectra., Comment: 8 pages

Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the adiabatic assumption. A Hamiltonian of such a system is affine in the temporal derivative of parameter functions. This leads to the geometric Berry factor phenomena., Comment: 20 pages

We show that non-relativistic and relativistic mechanical systems on a configuration space Q can be seen as the conservative Dirac constraint systems with zero Hamiltonians on different subbundles of the same cotangent bundle T^*Q. The geometric quantization of this cotangent bundle under the vertical polarization leads to compatible covariant quantizations of non-relativistic and relativistic Hamiltonian mechanics., Comment: 18 pages

We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the Schrodinger representation of V^*Q. We show that this quantization is equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R, that makes the quantum algebra of non-relativistic mechanics an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra, which provides quantum evolution in non-relativistic mechanics as a parallel transport along time., Comment: 17 pages

Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions., Comment: 17 pages

The iterated BRST cohomology is studied by computing cohomology of the variational complex on the infinite order jet space of a smooth fibre bundle. This computation also provides a solution of the global inverse problem of the calculus of variations in Lagrangian field theory., Comment: 15 pages

We obtain the cohomology of the variational bicomplex on the infinite order jet space of a smooth fiber bundle in the class of exterior forms of finite jet order. This provides a solution of the global inverse problem of the calculus of variations of finite order on fiber bundles., Comment: 18 pages

Cohomology of the variational bicomplex in the calculus of variations in classical field theory are computed in the class of exteriror forms of finite jet order. This provides a solution of the global inverse problem of the finite order calculus of variations., Comment: 21 pages

De Rham cohomology, $d_V$- and $d_H$-cohomology of the differential algebra of locally pull-back exterior forms on the infinite-order jet manifold of a smooth fibre bundle are calculated., Comment: 10 pages

We show that the cohomology groups of the horizontal (total) differential on horizontal (local) exterior forms on the infinite-order jet manifold of an affine bundle coincide with the De Rham cohomology groups of the base manifold. This prevents one from the topological obstruction to the definition of global descent equations in BRST theory on an arbitrary affine bundle., Comment: 11 pages, LaTeX

We study the obstruction to the exactness of the variational complex for a field theory on an affine bundle., Comment: 12 pages, LaTeX

It is emphasized that equivalent definitions of connections on modules over commutative rings are not so in noncommutative geometry., Comment: 29 pages, LaTeX

We show that, in the framework of covariant Hamiltonian field theory, a degenerate almost regular quadratic Lagrangian $L$ admits a complete set of non-degenerate Hamiltonian forms such that solutions of the corresponding Hamilton equations, which live in the Lagrangian constraint space, exhaust solutions of the Euler--Lagrange equations for $L$. We obtain the characteristic splittings of the configuration and momentum phase bundles. Due to the corresponding projection operators, the Koszul-Tate resolution of the Lagrangian constraints for a generic almost regular quadratic Lagrangian is constructed in an explicit form., Comment: 10 pages, LaTeX

It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$. The case of quadratic dynamic equations is analyzed in details. The equation for Jacobi vector fields is constructed and investigated by the geometric methods., Comment: 15 pages, LaTeX

We show that any second order dynamic equation on a configuration space $X\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\to X$ of relativistic velocities. We compare relativistic and nonrelativistic geodesic equations, and study the Jacobi vector fields along nonrelativistic geodesics., Comment: 17 pages, LaTeX

In Hamiltonian time-dependent mechanics, the Poisson bracket does not define dynamic equations, that implies the corresponding peculiarities of describing time-dependent holonomic constraints. As in conservative mechanics, one can consider the Poisson bracket of constraints, separate them in first and second class constraints, construct the Koszul-Tate resolution and a BRST complex. However, the Poisson bracket of constraints and a Hamiltonian makes no sense. Hamiltonian vector fields for first class constraints are not generators of gauge transformations. In the case of Lagrangian constraints, we state the comprehensive relations between solutions of the Lagrange equations for an almost regular Lagrangian and solutions of the Hamilton equations for associated Hamiltonian forms, which live in the Lagrangian constraint space. Degenerate quadratic Lagrangian systems are studied in details. We construct the Koszul-Tate resolution for Lagrangian constraints of these systems in an explicit form., Comment: 37 pages, LaTeX

We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries., Comment: 35 pages, Latex