$\kappa$-Poincaré invariant quantum field theories with KMS weight

Abstract

A natural star product for 4-d $\kappa$-Minkowski space is used to investigate various classes of $\kappa$-Poincaré invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual ${\varphi }^4$ theory. $\kappa$-Poincaré 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.

32 pages, several paragraphs added, published in PRD

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Cited by in corpus (19)

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• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Gauge theories on quantum spaces
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• $\kappa$-deformed complex fields and discrete symmetries
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Field theories on $\rho$-deformed Minkowski space-time
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Quantum causality constraints on kappa-Minkowski space-time
• Field Theory with Coordinate Dependent Noncommutativity
• Quantum causality in $\kappa$-Minkowski and related constraints
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Star-products for Lie-algebraic noncommutative Minkowski space-times