$\kappa$-Poincar\'e invariant quantum field theories with KMS weight

TL;DR

This paper explores $$-Poincare9 invariant quantum field theories on $$-Minkowski space, analyzing their algebraic structures, divergences, and UV/IR mixing phenomena, with implications for noncommutative geometry and quantum physics.

Contribution

It introduces a new framework for $$-Poincare9 invariant scalar field theories using KMS weights, characterizes their modular structures, and examines divergence and mixing behaviors.

Findings

Planar one-loop contributions are at most UV linearly divergent.

Some theories are free of UV/IR mixing.

Non-planar contributions exhibit polynomial singularities at zero external momenta.

Abstract

A natural star product for 4-d $\kappa$-Minkowski space is used to investigate various classes of $\kappa$-Poincar\'e invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual $\phi^4$ theory. $\kappa$-Poincar\'e invariance forces the integral involved in the actions to be a twisted trace, thus defining a KMS weight for the noncommutative (C*-)algebra modeling the $\kappa$-Minkowski space. The associated modular group and Tomita modular operator are characterized. In all the field theories, the twist generates different planar one-loop contributions to the 2-point function which are at most UV linearly diverging. Some of these theories are free of UV/IR mixing. In the others, UV/IR mixing shows up in non-planar contributions to the 2-point function as a polynomial singularity at exceptional zero external momenta while staying finite at non-zero external momenta. These results are discussed together with the possibility for the KMS weight relative to the quantum space algebra to trigger the appearance of KMS state on the algebra of observables.