Canonical k-Minkowski Spacetime

Abstract

A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically "radial", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at "large" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime.

30 pages, uses hyperref

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Cited by in corpus (6)

• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• A modular spectral triple for $\kappa$-Minkowski space
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Poincaré Covariant k-Minkowski Spacetime
• Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis