The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime

Abstract

We present a quantization of the functions of spacetime, i.e.\ a map, analog to Weyl map, which reproduces the $\kappa$-Minkowski commutation relations, and it has the desirable properties of mapping square integrable funcions into Hilbert-Schmidt operators, as well as real functions into self-adjoint operators. The map is based on Mellin transform on radial and time coordinates. The map also define a deformed $\ast$ product which we discuss with examples.

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Cited by in corpus (2)

• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance