Mass Renormalization for Time Dependent Correlation Functions in Shibata-Hashitsume's Projection Operator Method

TL;DR

This paper applies Shibata-Hashitsume's projection operator method to analyze the time evolution of correlation functions, addressing ultraviolet divergences through mass renormalization at both zero and finite temperatures.

Contribution

It introduces a mass renormalization approach for time-dependent correlation functions within the projection operator framework, handling divergences in a novel way.

Findings

Ultraviolet divergences are renormalized using a mass counter term.

A residual log t divergence remains at initial time after lowest order renormalization.

The method applies to both zero and finite temperature cases.

Abstract

We study the time development of correlation functions at both zero and finite temperature with Shibata-Hashitsume's projection operator method and carry out the renormalization of ultraviolet divergence that appears in a time-dependent frequency shift, using a mass counter term. A harmless divergence of log t-type remains at an initial time t=0 after the lowest order renormalization.