Thermofield Dynamics for Twisted Poincare-Invariant Field Theories: Wick Theorem and S-matrix

TL;DR

This paper develops a finite-temperature quantum field theory framework for twisted Poincare-invariant fields using Thermofield Dynamics, proving Wick's theorem for twisted scalar fields, thus enabling analysis of non-commutative quantum systems.

Contribution

It extends Thermofield Dynamics to twisted Poincare-invariant fields at finite temperature, including interacting fields, and proves Wick's theorem in this context.

Findings

Wick's theorem holds for twisted scalar fields at finite temperature.

Thermofield Dynamics can be extended to interacting twisted fields.

Framework enables finite-temperature analysis of non-commutative quantum field theories.

Abstract

Poincare invariant quantum field theories can be formulated on non-commutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincare group is suitably twisted. In the present work we present a twisted Poincare invariant quantum field theory at finite temperature. For that we use the formalism of Thermofield Dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a non trivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.