Causal signal transmission by quantum fields. II. Quantum-statistical response of interacting bosons

TL;DR

This paper introduces a nonperturbative response formulation for quantum fields, unifying relativistic and nonrelativistic models, and ensuring causality and consistency with established response theories.

Contribution

It develops a quantum-statistical response framework for interacting bosonic fields, extending previous formalisms and unifying various response theories in quantum field theory.

Findings

Response formulation preserves causality properties.

Unifies Schwinger's, Kubo's, and Glauber's theories.

Applicable to both relativistic and nonrelativistic models.

Abstract

We analyse nonperturbatively signal transmission patterns in Green's functions of interacting quantum fields. Quantum field theory is re-formulated in terms of the nonlinear quantum-statistical response of the field. This formulation applies equally to interacting relativistic fields and nonrelativistic models. Of crucial importance is that all causality properties to be expected of a response formulation indeed hold. Being by construction equivalent to Schwinger's closed-time-loop formalism, this formulation is also shown to be related naturally to both Kubo's linear response and Glauber's macroscopic photodetection theories, being a unification of the two with generalisation to the nonlinear quantum-statistical response problem. In this paper we introduce response formulation of bosons; response reformulation of fermions will be subject of a separate paper.