Gauge Theories on quantum Minkowski spaces: $ρ$ versus $κ$

The $ρ$-Minkowski space-time, a Lie-algebraic deformation of the usual Minkowski space-time is considered. A star-product realization of this quantum space-time together with the characterization of the deformed Poincaré symmetry acting on it are presented. It is shown that appearance of UV/IR mixing is expected already in scalar field theories on $ρ$-Minkowski. Classical and one-loop features of a typical gauge theory on this quantum space-time are presented and critically compared to the situation for $κ$-Minkowski.

💡 Research Summary

The paper presents a comprehensive study of the ρ‑Minkowski space‑time, a Lie‑algebraic deformation of ordinary Minkowski space, and compares its quantum field theoretic properties with those of the well‑studied κ‑Minkowski space‑time. The authors first construct a star‑product realization of ρ‑Minkowski by combining the Weyl quantization map with the convolution algebra of the Euclidean group SE(2), which is the Lie group associated with the coordinate algebra (