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- Title
Field theories on ρ-deformed Minkowski space-time.
- Authors
Hersent, Kilian; Wallet, Jean-Christophe
- 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.
- Subjects
SCALAR field theory; HAAR integral; GROUP algebras; SPACETIME; GEOMETRIC quantization; BANACH algebras; ALGEBRA
- Publication
Journal of High Energy Physics, 2023, Vol 2023, Issue 7, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP07(2023)031