# Spectral geometry of ?-Minkowski space

@article{DAndrea2005SpectralGO, title={Spectral geometry of ?-Minkowski space}, author={Francesco D’Andrea}, journal={Journal of Mathematical Physics}, year={2005} }

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…

## 23 Citations

### On the spectral and homological dimension of k-Minkowski space

- Mathematics
- 2013

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…

### κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

- 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…

### Dirac operators on noncommutative curved spacetimes

- 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…

### Kappa-Minkowski spacetime: mathematical formalism and applications in Planck scale physics

- Physics, Mathematics
- 2011

The dissertation presents possibilities of applying noncommutative spacetimes description, particularly kappa-deformed Minkowski spacetime and Drinfeld's deformation theory, as a mathematical…

### κ-Deformations and Extended κ-Minkowski Spacetimes

- 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…

### Gauge theory models on κ-Minkowski space: Results and prospects

- 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…

### Localization and reference frames in κ -Minkowski spacetime

- PhysicsPhysical 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…

### $\kappa$-Poincar\'e invariant quantum field theories with KMS weight

- 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…

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