QED in inhomogeneous magnetic fields

Abstract

A lower bound is placed on the fermionic determinant of Euclidean quantum electrodynamics in three dimensions in the presence of a smooth, finite--flux, static, unidirectional magnetic field $\mathbf{B}(\mathbf{r})=(0,0,B(\mathbf{r}))$, where $B(\mathbf{r})\ge 0$ or $B(\mathbf{r})\le 0$ and $\mathbf{r}$ is a point in the $xy\mbox{-plane}$. Bounds are also obtained for the induced spin for $2+1$ dimensional QED in the presence of $\mathbf{B}(\mathbf{r})$. An upper bound is placed on the fermionic determinant of Euclidean QED in four dimensions in the presence of a strong, static, directionally-varying, square-integrable magnetic field $\mathbf{B}(\mathbf{r})$ on ${\mathbb{R}}^3$.

20 pages, latex2e + amstex

References in corpus (6)

• Effective Energy for QED${}_{2+1}$ with Semi-Localized Static Magnetic Fields: A Solvable Model
• Inhomogeneous Condensates in Planar QED
• On chiral symmetry breaking by external magnetic fields in QED${}_3$
• Fermionic Determinant of the Massive Schwinger Model
• Fermion Determinants in Static, Inhomogeneous Magnetic Fields
• QED in strong, finite-flux magnetic fields

Cited by in corpus (19)

• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• Functional Determinants in Quantum Field Theory
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• Degeneracy of zero modes of the Dirac operator in three dimensions
• Paramagnetism, zero modes and mass singularities in QED in $1+1$, $2+1$ and $3+1$ dimensions
• Polarization of the vacuum of a quantized scalar field by an impenetrable magnetic vortex of finite thickness
• Induced vacuum energy-momentum tensor in the background of a d-2 - brane in d+1 - dimensional space-time
• Fermion determinant for general background gauge fields
• Zero modes in finite range magnetic fields
• Landau Levels of Scalar QED in Time-Dependent Magnetic Fields
• Mass zeros in the one-loop effective actions of QED in 1+1 and 3+1 dimensions
• Chiral limit of the two-dimensional fermionic determinant in a general magnetic field
• Chern-Simons action for zero-mode supporting gauge fields in three dimensions
• Induced vacuum energy density of quantum charged scalar matter in the background of an impenetrable magnetic tube with the Neumann boundary condition
• Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature
• Stability of QED
• The symmetries of the Dirac--Pauli equation in two and three dimensions