Chiral phase dependence of fermion partition function in two dimension

TL;DR

This paper investigates how the fermion partition function in two-dimensional space-time depends on chiral phase in a U(1) gauge background, providing a method for continuous spectra and analyzing phase dependence with asymptotic expansion.

Contribution

It introduces a precise method for calculating the fermion path integral with continuous spectra and derives the chiral phase dependence expansion up to next-to-next leading order.

Findings

Chiral phase dependence is primarily determined by the winding number of the background field.

Corrections to the phase dependence vanish up to the considered order.

A well-defined approach for the path integral in continuous spectra is established.

Abstract

The chiral phase dependence of fermion partition function in spherically symmetric U(1) gauge field background is analyzed in two dimensional space-time. A well-defined method to calculated the path integral which apply to the continuous fermion spectrum is described. The one-to-one correspondence between the nonzero energy continuous spectra of two pertinent hamiltonians, which are defined by the Dirac operator to make the path integral well-defined, is shown to be exact. The asymptotic expansion for the chiral phase dependence in \(1/|m|^2\) (\(m\) is mass of the fermion.) is proposed and the coefficients in the expansion are evaluated up to the next-to-next leading term. Up to this order, the chiral phase dependence is given only by the winding number of background field and the corrections vanish.