Quasiparticle excitations in relativistic quantum field theory

TL;DR

This paper investigates quasiparticle excitations in relativistic quantum field theories using spectral and real-time methods, revealing their energy and decay characteristics in non-vacuum states.

Contribution

It introduces two complementary methods to analyze quasiparticles in relativistic fields, linking their properties to self-energy components and comparing with existing approaches.

Findings

Quasiparticle energy and decay rate are given by the real and imaginary parts of the retarded self-energy.

Both methods yield consistent results for quasiparticle properties.

The analysis bridges spectral and real-time approaches, enhancing understanding of non-vacuum excitations.

Abstract

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.