Group velocity in noncommutative spacetime (original) (raw)

Particle velocity in noncommutative space-time

Physical Review D, 2002

We investigate a particle velocity in the κ-Minkowski space-time, which is one of the realization of a noncommutative space-time. We emphasize that arrival time analyses by high-energy γ-rays or neutrinos, which have been considered as powerful tools to restrict the violation of Lorentz invariance, are not effective to detect space-time noncommutativity. In contrast with these examples, we point out a possibility that low-energy massive particles play an important role to detect it. 95.85.Pw, 98.70.Sa.

Waves on Noncommutative Space–Time and Gamma-Ray Bursts

International Journal of Modern Physics A, 2000

Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski space–time [xi, t]=ιλxi. A natural wave equation is derived and the associated phenomena of in vacuo dispersion are discussed. Assuming the deformation scale λ is of the order of the Planck length one finds that the dispersion effects are large enough to be tested in experimental investigations of astrophysical phenomena such as gamma-ray bursts. We also outline a new approach to the construction of field theories on the noncommutative space–time, with the noncommutativity equivalent under Fourier transform to non-Abelianness of the "addition law" for momentum in Feynman diagrams. We argue that CPT violation effects of the type testable using the sensitive neutral-kaon system are to be expected in such a theory.

Observables and dispersion relations in κ-Minkowski spacetime

Journal of High Energy Physics

Observables and Dispersion Relations in k-Minkowski Spacetime

2017

We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of k-Minkowski spacetime. The corresponding quantum Poincare'-Weyl Lie algebra of infinitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

A no-pure-boost uncertainty principle from spacetime noncommutativity

Physics Letters B, 2009

We study boost and space-rotation transformations in κ-Minkowski noncommutative spacetime, using the techniques that some of us had previously developed (hep-th/0607221) for a description of translations in κ-Minkowski, which in particular led to the introduction of translation transformation parameters that do not commute with the spacetime coordinates. We find a similar description of boosts and space rotations, which allows us to identify some associated conserved charges, but the form of the commutators between transformation parameters and spacetime coordinates is incompatible with the possibility of a pure boost. * Supported by EU Marie Curie fellowship EIF-025947-QGNC

Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes

2003

In this thesis I study various aspects of theories in the two most studied examples of noncommutative spacetimes: canonical spacetime ($[x_{\mu},x_{\nu}]=\theta_{\mu\nu}$) and kappa\kappakappa-Minkowski spacetime ($[x_{i},t]=\kappa^{-1} x_{i}$). In the first part of the thesis I consider the description of the propagation of "classical" waves in these spacetimes. In the case of kappa\kappakappa-Minkowski this description is rather nontrivial, and its phenomenological implications

Gravitational measurements in Non-commutative spaces

2018

The general theory of relativity is the currently accepted theory of gravity and as such, a large repository of test results has been carried out since its inception in 1915. However, in this paper we will only focus on what are considered as the main tests but in non-commutative geometries. Using the coordinate coherent state formalism, we consider gravitational red-shift, deflection, and time delay of light, separately, for Schwarzschild and Riessner-Nordstrom metrics in their non-commutative form. We will schematically show that these non-commutative calculations have different behavior with respect to the predictions of general relativity. We also specify an upper bound on the non-commutative parameter by comparing the results with accuracies of gravitational measurements for typical micro black holes which can be produced in the early universe.

From noncommutative κ-Minkowski to Minkowski space–time

Physics Letters B, 2007

We show that free κ-Minkowski space field theory is equivalent to a relativistically invariant, non local, free field theory on Minkowski space-time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass m and a Planck mass tachyon. We show that while the energy momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.

Special relativity as a noncommutative geometry: Lessons for deformed special relativity

Physical Review D, 2010

Deformed Special Relativity (DSR) is obtained by imposing a maximal energy to Special Relativity and deforming the Lorentz symmetry (more exactly the Poincaré symmetry) to accommodate this requirement. One can apply the same procedure deforming the Galilean symmetry in order to impose a maximal speed (the speed of light). This leads to a non-commutative space structure, to the expected deformations of composition of speed and conservation of energy-momentum. In doing so, one runs into most of the ambiguities that one stumbles onto in the DSR context. However, this time, Special Relativity is there to tell us what is the underlying physics, in such a way that we can understand and interpret these ambiguities. We use these insights to comment on the physics of DSR.

Towards a first-principles approach to spacetime noncommutativity

Journal of Physics: …, 2007

Our main thesis in this note is that if spacetime noncommutativity is at all relevant in the quantum gravitational regime, there might be a canonical approach to pinning down its form. We start by emphasizing the distinction between an intrinsically noncommuting "manifold", i.e., one with noncommuting coordinate functions, on the one hand, and particles with noncommuting position operators, on the other. Focusing on the latter case, which, we feel, more adequately reflects the experimental nature of our knowledge of spacetime properties, we find that several complementary considerations point to a spin-dependent noncommutativity, which is confirmed in the single-particle sector of Dirac's theory, as well as in Fokker's relativistic "center-of-mass" prescription. Finally, we propose an extension of Jordan and Mukunda's work to gain a glimpse on the effect of curvature on position operator noncommutativity.

Group velocity in noncommutative spacetime (original) (raw)

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