On Quantization of Time-Dependent Systems with Constraints

The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose an independent way to derive the rules of quantization for these systems, starting from physical equivalent theory with trivial non-stationarity.Comment: 4 page

The relation between isotopic composition of argon and carbon in natural gases

The methods and results of determination of the argon and carbon isotope compositions of hydrocarbon gases of Mezozoic complexes of Western Siberia are presented. Based on the Ar-36, Ar-40, C-12, C-13 content of the various deposits and on the presumed mechanisms of entry of these isotopes into the deposits, it is concluded that formation of natural gas in some deposits included vertical migration from a lower complex

One-loop energy-momentum tensor in QED with electric-like background

We have obtained nonperturbative one-loop expressions for the mean energy-momentum tensor and current density of Dirac's field on a constant electric-like background. One of the goals of this calculation is to give a consistent description of back-reaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contributions are related to the Heisenberg-Euler Lagrangian. Then, we study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the back-reaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.Comment: 35 pages; misprints in the sign in definitions (40)-(43), and (68) corrected, results unchange

On "Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field"

Recently the paper "Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field" by G. C. Nayak was published [Eur. Phys. J. C 59, 715 (2009); arXiv:0708.2430]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the so-called "shift theorem" [arXiv:hep-th/0609192] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.Comment: 4 page

Coherent and semiclassical states in magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane, this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS, which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and the time dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2+1)- and (3+1)- dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.Comment: 35 pages, 2 figures. Some typos in (77), (101), and (135) corrected with respect to the published version. Results unchange

Quantum scalar field in FRW Universe with constant electromagnetic background

We discuss massive scalar field with conformal coupling in Friedmann-Robertson-Walker (FRW) Universe of special type with constant electromagnetic field. Treating an external gravitational-electromagnetic background exactly, at first time the proper-time representations for out-in, in-in, and out-out scalar Green functions are explicitly constructed as proper-time integrals over the corresponding (complex) contours. The vacuum-to-vacuum transition amplitudes and number of created particles are found and vacuum instability is discussed. The mean values of the current and energy-momentum tensor are evaluated, and different approximations for them are investigated. The back reaction of the particles created to the electromagnetic field is estimated in different regimes. The connection between proper-time method and effective action is outlined. The effective action in scalar QED in weakly-curved FRW Universe (De Sitter space) with weak constant electromagnetic field is found as derivative expansion over curvature and electromagnetic field strength. Possible further applications of the results are briefly mentioned.Comment: 38 pages, LaTe

Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation

The D-dimensional cosmological model on the manifold $M = R \times M_{1} \times M_{2}$ describing the evolution of 2 Einsteinian factor spaces, $M_1$ and $M_2$, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of the perfect fluid components are both equal to 2, the Einstein equations for the model are reduced to the generalized Emden-Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin within discrete-group analysis. Using the integrable classes of this equation one generates the integrable cosmological models. The corresponding metrics are presented. The method is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$ and the 2-component perfect fluid source.Comment: LaTeX file, no figure

Quantization of Point-Like Particles and Consistent Relativistic Quantum Mechanics

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of the Hilbert space. It allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization a consistent relativistic quantum mechanics, which reproduces literally the behavior of the one-particle sector of the corresponding quantum field. In particular, in a physical sector of the Hilbert space a complete positive spectrum of energies of relativistic particles and antiparticles is reproduced, and all state vectors have only positive norms.Comment: 57 pages, LaTex fil