The effect of nonlocal confining kernels on magnetic chiral condensates

TL;DR

This paper investigates how nonlocal confining kernels influence magnetic chiral condensates, using Valatin-Bogoliubov transformations to analyze spontaneous chiral symmetry breaking under magnetic fields in various dimensions.

Contribution

It introduces a method to analyze the effects of nonlocal kernels on chiral condensates with magnetic fields, extending previous local kernel studies.

Findings

Nonlocal kernels significantly affect chiral condensate behavior.

Valatin-Bogoliubov transformations effectively diagonalize the Hamiltonian.

Results apply to both 2+1 and 3+1 dimensional systems.

Abstract

The physics of spontaneous chiral symmetry breaking in the case of the simultaneous presence of a magnetic field and a fermionic quartic interaction is discussed for both local and nonlocal kernels in 2+1 and 3+1 dimensions. The approach is based on the use of Valatin-Bogoliubov canonical transformations, which allow, in the absence of fermionic quartic terms, to completely diagonalize the Hamiltonian and construct the vacuum state.