# On κ-deformation and UV/IR mixing

@article{Grosse2006OnA, title={On $\kappa$-deformation and UV/IR mixing}, author={Harald Grosse and Michael Wohlgenannt}, journal={Nuclear Physics}, year={2006}, volume={748}, pages={473-484} }

We examine the UV/IR mixing property on a κ-deformed Euclidean space for a real scalar ϕ4 theory. All contributions to the tadpole diagram are explicitly calculated. UV/IR mixing is present, though in a different dressing than in the case of the canonical deformation.

## 53 Citations

UV/IR duality in noncommutative quantum field theory

- Physics, Mathematics
- 2011

We review the construction of renormalizable noncommutative Euclidean ϕ4-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended…

Commutation Relations and Ultraviolet/Infrared Mixing

- Mathematics
- 2009

We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic…

UV/IR mixing in noncommutative SU(N) Yang–Mills theory

- PhysicsThe European Physical Journal C
- 2021

We show that there are one-loop IR singularities arising from UV/IR mixing in noncommutative SU(N) Yang–Mills theory defined by means of the $$\theta $$
θ
-exact Seiberg–Witten map. This is in…

Translation invariance, commutation relations and ultraviolet/infrared mixing

- Physics
- 2009

We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic…

Vacuum energy and the cosmological constant problem in
κ
-Poincaré invariant field theories

- PhysicsPhysical Review D
- 2019

We investigate the vacuum energy in κ-Poincare invariant field theories. It is shown that for the equivariant Dirac operator one obtains an improvement in UV behavior of the vacuum energy and…

High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing

- Physics
- 2010

We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which – in contrast to the well known Moyal-Weyl…

UV-IR mixing in nonassociative Snyder ϕ^4 theory

- Physics
- 2018

Using a quantization of the nonassociative and noncommutative Snyder ϕ4 scalar field theory in a Hermitian realization, we present in this article analytical formulas for the momentum-conserving part…

Loop diagrams in space with SU(2) fuzziness

- Physics
- 2008

Abstract The structure of loop corrections is examined in a scalar field theory on a three-dimensional space whose spatial coordinates are noncommutative and satisfy SU(2) Lie algebra. In particular,…

Field theory amplitudes in a space with SU(2) fuzziness

- Physics
- 2008

The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined.…

On κ-deformation and triangular quasibialgebra structure

- Physics
- 2009

Abstract We show that, up to terms of order κ −5 , the κ-deformed Poincare algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given…

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