Finite field-energy of a point charge in QED

We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, which possesses a regularizing ability sufficient to make the field energy of a point charge finite. The model is exactly solved in the class of static central-symmetric electric fields. Collation with quantum electrodynamics (QED) results in the total field energy about twice the electron mass. The proof of the finiteness of the field energy is extended to include any polynomial selfinteraction, thereby the one that stems from the truncated expansion of the Euler-Heisenberg local Lagrangian in QED in powers of the field strenth

Canonical and D-transformations in Theories with Constraints

A class class of transformations in a super phase space (we call them D-transformations) is described, which play in theories with second-class constraints the role of ordinary canonical transformations in theories without constraints.Comment: 16 pages, LaTe

Noncommutative reduction of nonlinear Schrödinger equation on Lie groups

We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations. The main idea is to apply the method of noncommutative integration to the linear part of a nonlinear equation, which allows one to find bases in the space of solutions of linear partial differential equations with a set of noncommuting symmetry operators. The approach is implemented for the generalized nonlinear Schrödinger equation on a Lie group in curved space with local cubic nonlinearity. General formalism is illustrated by the example of the noncommutative reduction of the nonstationary nonlinear Schrödinger equation on the motion group E(2) of the two-dimensional plane R2. In this particular case, we come to the usual (1+1)-dimensional nonlinear Schrödinger equation with the soliton solution. Another example provides the noncommutative reduction of the stationary multidimensional nonlinear Schrödinger equation on the four-dimensional exponential solvable group

Statistical properties of states in QED with unstable vacuum

We study statistical properties of states of massive quantized charged Dirac and Klein-Gordon fields interacting with a background that violates the vacuum stability, first in general terms and then for a special electromagnetic background. As a starting point, we use a nonperturbative expression for the density operators of such fields derived by Gavrilov et al. [Gavrilov, Gitman, and Tomazelli, Nucl. Phys. B 795, 645 (2008)]. We construct the reduced density operators for electron and positron subsystems and discuss a decoherence that may occur in the course of the evolution due to an intermediate measurement. By calculating the entropy we study the loss of the information in QED states due to partial reductions and a possible decoherence. We consider the so-called T-constant external electric field as an external background. This exactly solvable example allows us to calculate explicitly all statistical properties of various quantum states of the massive charged fields under consideration

Peculiarities of pair creation by a peak electric field

Exact, numerical, and asymptotic calculations concerning the vacuum instability by the so-called peak electric field are explored in detail. Peculiarities discussed in this article are complementary to those published recently by us in Eur. Phys. J. C, 76, p. 447 (2016), in which the effect was studied in the framework of QED with t -electric potential steps. To discuss features beyond the asymptotic regime, we present numerical details of exact and asymptotic expressions inherent to the peak field and discuss differential and total quantities. The results show wider distributions, with respect to the longitudinal momentum, as the phases k1 and k2 of the electric field decrease and larger distributions as the amplitude E increases. Moreover, the total density of pairs created decreases as k1 and k2 increase, its dependence being proportional to k1 –1 and k2 –1. The latter result is more accurate as k1 and k2 decrease and confirms, in particular, our asymptotic estimates obtained previously

Spinor and Isospinor Structure of Relativistic Particle Propagators

Representations by means of path integrals are used to find spinor and isospinor structure of relativistic particle propagators in external fields. For Dirac propagator in an external electromagnetic field all grassmannian integrations are performed and a general result is presented via a bosonic path integral. The spinor structure of the integrand is given explicitly by its decomposition in the independent $\gamma$-matrix structures. Similar technique is used to get the isospinor structure of the scalar particle propagator in an external non-Abelian field.Comment: 9 pages, Preprint IC/93/197 Triest

Spin Factor in Path Integral Representation for Dirac Propagator in External Fields

We study the spin factor problem both in $3+1$ and $2+1$ dimensions which are essentially different for spin factor construction. Doing all Grassmann integrations in the corresponding path integral representations for Dirac propagator we get representations with spin factor in arbitrary external field. Thus, the propagator appears to be presented by means of bosonic path integral only. In $3+1$ dimensions we present a simple derivation of spin factor avoiding some unnecessary steps in the original brief letter (Gitman, Shvartsman, Phys. Lett. {\bf B318} (1993) 122) which themselves need some additional justification. In this way the meaning of the surprising possibility of complete integration over Grassmann variables gets clear. In $2+1$ dimensions the derivation of the spin factor is completely original. Then we use the representations with spin factor for calculations of the propagator in some configurations of external fields. Namely, in constant uniform electromagnetic field and in its combination with a plane wave field.Comment: 34 pages, LaTe