Spectral function of the Bloch-Nordsieck model at finite temperature

TL;DR

This paper calculates the exact fermionic spectral function of the Bloch-Nordsieck model at finite temperature, revealing its finite, normalizable nature and time-dependent behavior, with both analytical and numerical results.

Contribution

It provides the first exact finite-temperature spectral function for the model, including analytical solutions for special cases and numerical analysis for general parameters.

Findings

Spectral function is finite and normalizable at nonzero temperature.

Real-time Green's function shows power-law decay at small times and exponential damping at large times.

Temperature acts as an infrared regulator, enabling a safe zero-temperature interpretation.

Abstract

In this paper we determine the exact fermionic spectral function of the Bloch-Nordsieck model at finite temperature. Analytic results are presented for some special parameters, for other values we have numerical results. The spectral function is finite and normalizable for any nonzero temperature values. The real time dependence of the retarded Green's function is power-like for small times and exhibits exponential damping for large times. Treating the temperature as an infrared regulator, we can also give a safe interpretation of the zero temperature result.