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

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

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.

Propagators and Matrix Basis on Noncommutative Minkowski Space

We describe an analytic continuation of the Euclidean Grosse-Wulkenhaar and LSZ models which defines a one-parameter family of duality covariant noncommutative field theories interpolating between Euclidean and Minkowski space versions of these models, and provides an alternative regularization to the usual Feynman prescription. This regularization allows for a matrix model representation of the field theories in terms of a complex generalization of the usual basis of Landau wavefunctions. The corresponding propagators are calculated and identified with the Feynman propagators of the field theories. The regulated quantum field theories are shown to be UV/IR-duality covariant. We study the asymptotics of the regularized propagators in position and matrix space representations, and confirm that they generically possess a comparably good decay behaviour as in the Euclidean case.Comment: 45 pages; v2: clarifying comments added; v3: further clarifying comments added; Final version published in Physical Review

Magnetic Color Flavor Locking Phase in High Density QCD

We investigate the effects of an external magnetic field in the gap structure of a color superconductor with three massless quark flavors. Using an effective theory with four-fermion interactions, inspired by one-gluon exchange, we show that the long-range component $\widetilde{B}$ of the external magnetic field that penetrates the color-flavor locked (CFL) phase modifies its gap structure, producing a new phase of lower symmetry. A main outcome of our study is that the $\widetilde{B}$ field tends to strengthen the gaps formed by $\widetilde{Q}$-charged and $\widetilde{Q}$-neutral quarks that coupled among themselves through tree-level vertices. These gaps are enhanced by the field-dependent density of states of the $\widetilde{Q}$-charged quarks on the Fermi surface. Our considerations are relevant for the study of highly magnetized compact stars.Comment: version to be published in PR