arXiv subjects

V. I. Lapushkin

Publications and source records attributed to V. I. Lapushkin.

4 recordsLinked to original sources

arXiv2026

Surprises of Klein paradox

We consider second quantized $1+1$ dimensional Dirac fermions with mass $m$ in background electric fields. This theory mimics the following situations. We consider two parallel capacitors with opposite directions of the electric field $E$ in them. The potential energy difference in one of them is equal to $V_0 > 2m$ and in the other to $V+V_0$, with $0 2m$. We also consider the same theory in the presence of the infinite wall and a deep well $V_0>2m$. We show that in such a potential the limiting expectation value of the current is zero in the Gaussian approximation. We discuss the relation of these observations to the Schwinger effet and to the decay of supercritical nuclei.

hep-th↗

arXiv2025

Lessons from the Klein paradox

We re-examine the Klein paradox from a many-particle perspective in quantum field theory. Specifically, we compute the expectation value of the particle current induced by a sufficiently strong step-like electric potential in 1+1 dimensions. First, for a constant (eternal) potential, we calculate the current for different Fock space ground states corresponding to distinct mode bases. While one basis yields a zero current, another produces the standard nonzero value. We then consider a potential that is rapidly switched on, recovering the standard current in the asymptotic future. This result is generalized to potentials that interpolate between different constant values at spatial infinity. Finally, we analyze a potential acting for a finite duration and again reproduce the standard current. A physical interpretation of these results is provided.

hep-th↗

arXiv2025

Simplification of nonlinear equations for a field operator

In this paper, we study different properties of the motion equations of interacting fields. In the second section, we prove that "Wightman's" fields (we use only a subset of Wightman's axioms) are unitarily equivalent to some operators on the vector space ${\cal F}$ (with one mathematical assumption). In the third section, we introduce $L^{\infty}$ and $DL$ Hilbert spaces, which are convenient for analyzing field equations, particularly the equations for $ϕ^3$ theory. Remarkably, we have managed to reduce the equation of motion for $ϕ^3$ to a quadratic matrix equation with matrices over a separable Hilbert space in the fourth section. Also, in the appendix, we have done the same for QCD. Furthermore, we prove the existence of solution to the motion equations of one toy model non-renormalizable theory in the fifth section.

math-ph↗

arXiv2024

Light fields in various patches of de Sitter space-time

We start with the consideration of the loop effects for light fields with non-zero mass in the expanding Poincaré patch of de Sitter space-time. We derive the Dyson-Schwinger equation, which sums up the leading infrared (growing with time) loop corrections in certain limit for small initial perturbations above the Bunch-Davies state. The solution of this equation shows the destiny of the initial state at the future infinity. Then we discuss the case of the contracting Poincaré patch and global de Sitter space-time and briefly the case of different initial conditions in the expanding Poincaré patch.

hep-th↗