κ -Poincaré invariant quantum field theories with Kubo-Martin-Schwinger weight

A natural star product for 4-d κ-Minkowski space is used to investigate various classes of κ-Poincaré invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual ϕ4 theory. κ-Poincaré invariance forces the integral involved in the actions to be a twiste...

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Published in:Physical review. D 2018-07, Vol.98 (2), Article 025002
Main Authors: Poulain, Timothé, Wallet, Jean-Christophe
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Language:English
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Algebra
Invariants
Minkowski space
Quantum theory
Weight
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description A natural star product for 4-d κ-Minkowski space is used to investigate various classes of κ-Poincaré invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual ϕ4 theory. κ-Poincaré invariance forces the integral involved in the actions to be a twisted trace, thus defining a Kubo-Martin-Schwinger (KMS) weight for the noncommutative (C*-)algebra modeling the κ-Minkowski space. 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 at exceptional zero external momenta while staying finite at nonzero 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.
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source American Physical Society:Jisc Collections:APS Read and Publish 2023-2025 (reading list)
subjects Algebra
Invariants
Minkowski space
Quantum theory
Weight
title κ -Poincaré invariant quantum field theories with Kubo-Martin-Schwinger weight
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