Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Jean-Christophe Wallet

TL;DR

This paper investigates the ρ-Minkowski Lie-algebraic deformation of four-dimensional Minkowski space, constructing a Weyl-quantization–based star product via SE(2) convolution and deriving a deformed Poincaré Hopf algebra acting as twisted derivations. It analyzes UV/IR mixing in one-loop scalar φ^4 theories (orientable and non-orientable) and develops a gauge theory on ρ-Minkowski using a twisted differential calculus and a Koszul-type connection, yielding a gauge-invariant action that reduces to standard QED in the commutative limit. A notable result is the emergence of a non-vanishing tadpole under BRST gauge fixing, signaling potential vacuum effects or symmetry breaking, and the discussion contrasts ρ with κ-Minkowski in terms of trace structure and dimensional constraints. Overall, the work clarifies the mathematical structure of ρ-Minkowski and its physical consequences for noncommutative gauge theories relevant to quantum gravity.

Abstract

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.

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

TL;DR

This paper investigates the ρ-Minkowski Lie-algebraic deformation of four-dimensional Minkowski space, constructing a Weyl-quantization–based star product via SE(2) convolution and deriving a deformed Poincaré Hopf algebra acting as twisted derivations. It analyzes UV/IR mixing in one-loop scalar φ^4 theories (orientable and non-orientable) and develops a gauge theory on ρ-Minkowski using a twisted differential calculus and a Koszul-type connection, yielding a gauge-invariant action that reduces to standard QED in the commutative limit. A notable result is the emergence of a non-vanishing tadpole under BRST gauge fixing, signaling potential vacuum effects or symmetry breaking, and the discussion contrasts ρ with κ-Minkowski in terms of trace structure and dimensional constraints. Overall, the work clarifies the mathematical structure of ρ-Minkowski and its physical consequences for noncommutative gauge theories relevant to quantum gravity.

Abstract

The -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 -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 -Minkowski.

Paper Structure

This paper contains 6 sections, 57 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Star-product and involution for $\rho$-Minkowski
  3. $\rho$-deformed relativistic symmetries: The $\rho$-Poincaré algebra
  4. One-loop exploration of $\phi^4$ scalar field theory on $\rho$-Minkowski
  5. A gauge theory model on $\rho$-Minkowski
  6. Discussion and outlook

Figures (3)

  • Figure 1: Diagrams contributing to the 2-point function -- Orientable interaction.
  • Figure 2: Diagrams contribution to the 2-point function -- Non orientable interaction
  • Figure 3: Two diagrams contributing to the 4-point function -- Orientable interaction.