Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing

Abstract

We revisit the problem of quantizing field theories on noncommutative Moyal spacetime with \emph{light-like} noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, $p^{+}$. Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.

19 pages

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Cited by in corpus (5)

• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Noncommutative field with constant background fields and neutral fermion
• Noncommutative Time in Quantum Field Theory
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• On Light-like Deformations of the Poincaré Algebra