# Spectral geometry of ?-Minkowski space

@article{DAndrea2005SpectralGO,
title={Spectral geometry of ?-Minkowski space},
author={Francesco D’Andrea},
journal={Journal of Mathematical Physics},
year={2005}
}
• F. D’Andrea
• Published 1 March 2005
• Mathematics
• Journal of Mathematical Physics
After recalling Snyder’s idea [Phys. Rev. 71, 38 (1947)] of using vector fields over a smooth manifold as “coordinates on a noncommutative space,” we discuss a two-dimensional toy-model whose “dual” noncommutative coordinates form a Lie algebra: this is the well-known κ-Minkowski space [Phys. Lett. B 334, 348 (1994)]. We show how to improve Snyder’s idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of κ-Minkowski as…
We extend the construction of a spectral triple for k-Minkowski space, previously given for the two-dimensional case, to the general n-dimensional case. This takes into account the modular group
• Mathematics
• 2010
Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal frame- work of deformed Weyl-Heisenberg
• Mathematics
• 2013
We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms
The dissertation presents possibilities of applying noncommutative spacetimes description, particularly kappa-deformed Minkowski spacetime and Drinfeld's deformation theory, as a mathematical
• Mathematics
• 2014
We extend our previous study of Hopf-algebraic $\kappa$-deformations of all inhomogeneous orthogonal Lie algebras ${\rm iso}(g)$ as written in a tensorial and unified form. Such deformations are
• Physics
• 2022
Recent results obtained in κ-Poincaré invariant gauge theories on κ-Minkowski space are reviewed and commented. A Weyl quantization procedure can be applied to convolution algebras to derive a
• Physics
Physical Review D
• 2019
We study the limits to the localizability of events and reference frames in the $\kappa$-Minkowski quantum spacetime. Our main tool will be a representation of the $\kappa$-Minkowski commutation
• Mathematics
• 2018
A natural star product for 4-d $\kappa$-Minkowski space is used to investigate various classes of $\kappa$-Poincar\'e invariant scalar field theories with quartic interactions whose commutative limit

## References

SHOWING 1-10 OF 21 REFERENCES

• Mathematics
• 2002
While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x i ,x j ] = iθ ij . Here we present new
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds. Its unitary representations correspond
Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In
• Mathematics, Physics
• 1993
For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one
• Mathematics
• 2003
Abstract.A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (the Poincaré
Derivation of κ -Poincare bicovariant commutation relations between coordinates and 1-forms on κ -Minkowski space is given using Dirac operator and Allain Connes formula. The deformed U (1) gauge
Connections between the -Poincare covariant space of differential 1-forms on -Minkowski space, Dirac operator and Alain Connes formula are studied. The equations and Lagrangian of gauge theory are
• Mathematics
• 2004
Axioms for nonunital spectral triples, extending those introduced in the unital case by Connes, are proposed. As a guide, and for the sake of their importance in noncommutative quantum field theory,
A model of Euclidean spacetime is presented in which at scales less than a certain length kappa the notion of a point does not exist and the algebra which determines the structure of the model is an algebra of matrices.
• Physics
• 1997
We describe the deformed covariant phase space corresponding to the so-called kappa-deformation of D=4 relativistic symmetries, with quantum time'' coordinate and Heisenberg algebra obtained