QED in inhomogeneous magnetic fields

TL;DR

This paper establishes bounds on the fermionic determinant and induced spin in Euclidean quantum electrodynamics across three and four dimensions, considering inhomogeneous magnetic fields with specific properties.

Contribution

It provides new bounds on the fermionic determinant and induced spin in QED with inhomogeneous magnetic fields in 2+1 and 3+1 dimensions, extending previous analyses.

Findings

Lower bounds on fermionic determinants in 3D QED with magnetic fields.

Upper bounds on fermionic determinants in 4D QED with magnetic fields.

Bounds on induced spin in 2+1 dimensional QED.

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 $B(\mathbf{r})\geq 0$ or $B(\mathbf{r})\leq 0$ 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 $\R^3 $.