We consider the time evolution of a quantized field in backgrounds that violate the vacuum stability (particle-creating backgrounds). Our aim is to study the exact form of the final quantum state (the density operator at a final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of the evolution. We find a generating functional that allows us to have the density operators for any initial state. Averaging over states of a subsystem of antiparticles (particles), we obtain explicit forms for reduced density operators for subsystems of particles (antiparticles). Studying one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g. gluons) in an initial state increases the creation rate of the same kind of bosons. We discuss the question (and its relation to the initial stage of quark-gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not a thermal equilibrium. In this respect, we discuss some cases when a pair creation by an electric-like field can mimic a one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we study the time and temperature behavior of mean numbers of created particles provided switching on and off effects of the external field are negligible. It is shown that at high temperatures and in slowly varying electric fields the rate of particle creation is essentially time-dependent.
In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the HamiltonJacobi equation for such systems, analizing the singular case in order to obtain the equations of motion as total differential equations and study the integrability conditions for such equations. An example is solved using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results are compared.
In this paper we introduce a current-current type interaction term in the Lagrangian density of gravity coupled to complex scalar fields, in the presence of a degenerated Fermi gas. For low transferred momenta, such a term, which might account for the interaction among boson and fermion constituents of compact stellar objects, is subsequently reduced to a quadratic one in the scalar sector. This procedure enforces the use of a complex radial field counterpart in the equations of motion. The real and the imaginary components of the scalar field exhibit different behavior as the interaction increases. The results also suggest that the Bose-Fermi system undergoes a phase transition for a suitable choice of the coupling constant. ͓S0556-2821͑98͒07720-0͔ PACS number͑s͒: 95.30.Sf, 98.80.Cq
We evaluate the one-loop vacuum polarization tensor for three-dimensional quantum electrodynamics (QED), using an analytic regularization technique, implemented in a gauge-invariant way. We show thus that a gauge boson mass is generated at this level of radiative correction to the photon propagator. We also point out in our conclusions that the generalization for the non Abelian case is straightforward.
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