Abstract
We study one-loop perturbative properties of scalar field theories on the ρ-Minkowski space. The corresponding star-product, together with the involution are characterized from a combination of Weyl quantization and defining properties of the convolution algebra of the Euclidean group linked to the coordinate algebra of the ρ-Minkowski space. The natural integration measure linked to the Haar measure of the Euclidean group defines a trace for the star-product. One-loop properties of the 2-point and 4-point functions for families of complex-valued scalar field theories on ρ-Minkowski space are examined. For scalar theories with orientable interaction, the 2-point function is found to receive UV quadratically diverging one-loop corrections in 4 dimensions while no IR singularities generating UV/IR mixing appears. These however occur in the one-loop corrections to the 4-point function. As well, one-loop 2-point functions for theories with non-orientable interaction involve such IR singularities. These results are discussed.
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Acknowledgments
We thank P. Vitale for discussions on ρ-Minkowski space and related noncommutative field theories. J.-C. W is grateful to A. Wallet for numerous discussions on various aspects of harmonic analysis of locally compact groups.
We thanks the Action CA18108 QG-MM “Quantum Gravity phenomenology in the multi-messenger approach” and the Action 21109 CaLISTA “Cartan geometry, Lie, Integrable Systems, quantum group Theories for Applications”, from the European Cooperation in Science and Technology.
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Hersent, K., Wallet, JC. Field theories on ρ-deformed Minkowski space-time. J. High Energ. Phys. 2023, 31 (2023). https://doi.org/10.1007/JHEP07(2023)031
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DOI: https://doi.org/10.1007/JHEP07(2023)031