Common vacuum conservation amplitude in the theory of the radiation of mirrors in two-dimensional space-time and of charges in four-dimensional space-time

The action changes (and thus the vacuum conservation amplitudes) in the proper-time representation are found for an accelerated mirror interacting with scalar and spinor vacuum fields in 1+1 space. They are shown to coincide to within the multiplier e^2 with the action changes of electric and scalar charges accelerated in 3+1 space. This coincidence is attributed to the fact that the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0 as do the photons and scalar quanta emitted by charges. It is shown that the propagation of virtual pairs in 1+1 space can be described by the causal Green's function \Delta_f(z,\mu) of the wave equation for 3+1 space. This is because the pairs can have any positive mass and their propagation function is represented by an integral of the causal propagation function of a massive particle in 1+1 space over mass which coincides with \Delta_f(z,\mu). In this integral the lower limit \mu is chosen small, but nonzero, to eliminate the infrared divergence. It is shown that the real and imaginary parts of the action change are related by dispersion relations, in which a mass parameter serves as the dispersion variable. They are a consequence of the same relations for \Delta_f(z,\mu). Therefore, the appearance of the real part of the action change is a direct consequence of the causality, according to which real part of \Delta_f(z,\mu) is nonzero only for timelike and zero intervals.Comment: 23 pages, Latex, revte

Symmetries and causes of the coincidence of the radiation spectra of mirrors and charges in 1+1 and 3+1 spaces

This paper discusses the symmetry of the wave field that lies to the right and left of a two-sided accelerated mirror in 1 + 1 space and satisfies a single condition on it. The symmetry is accumulated in the Bogolyubov matrix coefficients $\alpha$ and $\beta$ that connect the two complete sets of solutions of the wave equations. The amplitudes of the quantum processes in the right and left half-spaces are expressed in terms of $\alpha$ and $\beta$ and are related to each other by transformation (12). Coefficient $\beta_{\omega'\omega}^*$ plays the role of the source amplitude of a pair of particles that are directed to opposite sides with frequencies $\omega$ and $\omega'$ but that are in either the left or the right half-space as a consequence of the reflection of one of them. Such an interpretation makes $\beta_{\omega'\omega}^*$ observable and explains the equalities, given by Eq. (1) and found earlier by Nikishov and author [Zh. Eksp. Teor. Fiz. 108, 1121 (1995)] and by author [Zh. Eksp. Teor. Fiz. 110, 526 (1996)] that the radiation spectra of a mirror in 1+1 space coincide with those of charges in 3 + 1 space by the fact that the moment of the pair emitted by the mirror coincide with the spin of the single particle emitted by the charge.Comment: 18 pages, LaTe

Dynamically Induced Zeeman Effect in Massless QED

It is shown that in non-perturbative massless QED an anomalous magnetic moment is dynamically induced by an applied magnetic field. The induced magnetic moment produces a Zeeman splitting for electrons in Landau levels higher than $l=0$. The expressions for the non-perturbative Lande g-factor and Bohr magneton are obtained. Possible applications of this effect are outlined.Comment: Extensively revised version with several misprints and formulas corrected. In this new version we included the non-perturbative Lande g-factor and Bohr magneto

Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions

We calculate the condensate and the vacuum current density induced by external static magnetic fields in (2+1)-dimensions. At the perturbative level, we consider an exponentially decaying magnetic field along one cartesian coordinate. Non-perturbatively, we obtain the fermion propagator in the presence of a uniform magnetic field by solving the Schwinger-Dyson equation in the rainbow-ladder approximation. In the large flux limit, we observe that both these quantities, either perturbative (inhomogeneous) and non-perturbative (homogeneous), are proportional to the external field, in agreement with early expectations.Comment: 8 pages, 2 figures. Accepted for publication in Phys. Rev.

The probability distribution of the number of electron-positron pairs produced in a uniform electric field

The probability-generating function of the number of electron-positron pairs produced in a uniform electric field is constructed. The mean and variance of the numbers of pairs are calculated, and analytical expressions for the probability of low numbers of electron-positron pairs are given. A recursive formula is derived for evaluating the probability of any number of pairs. In electric fields of supercritical strength |eE| > \pi m^2/ \ln 2, where e is the electron charge, E is the electric field, and m is the electron mass, a branch-point singularity of the probability-generating function penetrates the unit circle |z| = 1, which leads to the asymptotic divergence of the cumulative probability. This divergence indicates a failure of the continuum limit approximation. In the continuum limit and for any field strength, the positive definiteness of the probability is violated in the tail of the distribution. Analyticity, convergence, and positive definiteness are restored upon the summation over discrete levels of electrons in the normalization volume. Numerical examples illustrating the field strength dependence of the asymptotic behavior of the probability distribution are presented.Comment: 7 pages, REVTeX, 4 figures; new references added; a short version of this e-print has appeared in PR

Consistency restrictions on maximal electric field strength in QFT

QFT with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its duration in QED and QCD, we analyze the mean energy density of quantized fields for an arbitrary constant electric field E, acting during a large but finite time T. Using the corresponding asymptotics with respect to the dimensionless parameter $eET^2$, one can see that the leading contributions to the energy are due to the creation of paticles by the electric field. Assuming that these contributions are small in comparison with the energy density of the electric background, we establish the above-mentioned restrictions, which determine, in fact, the time scales from above of depletion of an electric field due to the backreactionComment: 7 pages; version accepted for publication in Phys. Rev. Lett.; added one ref. and some comment