Field theories on $\rho$-deformed Minkowski space-time

Abstract

We study one-loop perturbative properties of scalar field theories on the $\rho$-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 $\rho$-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 $\rho$-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.

arXiv comment19 pages

References in corpus (29)

• Quantum Field Theory on Noncommutative Spaces
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• D-branes and Deformation Quantization
• Doubly Special Relativity
• The principle of relative locality
• Introduction to Doubly Special Relativity
• Deformed Field Theory on kappa-spacetime
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Infinitely many star products to play with
• On $\kappa$-Deformation and UV/IR Mixing
• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Noncommutative field theory from angular twist
• Quantum gauge theories on noncommutative 3-d space
• Noncommutative scalar field in the non-extremal Reissner-Nordström background: QNM spectrum
• A twisted look on kappa-Minkowski: U(1) gauge theory
• Noncommutative $R^d$ via closed star product
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Gauge theories on quantum spaces
• Star product realizations of kappa-Minkowski space
• Field theory on kappa-spacetime
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• Kappa-Deformations: Historical Developments and Recent Results
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Time Discretization From Noncommutativity
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• Localization and observers in $\varrho$-Minkowski spacetime

Cited by in corpus (3)

• Formal developments in curved momentum space: the quantum field theory roadmap
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Star-products for Lie-algebraic noncommutative Minkowski space-times