Particle velocity in noncommutative space-time (original) (raw)

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.

Have we already detected astrophysical symptoms of space-time noncommutativity?

Physical Review D, 2002

We discuss astrophysical implications of κ-Minkowski space-time, in which there appears spacetime noncommutativity. We first derive a velocity formula for particles based on the motion of a wave packet. The result is that a massless particle moves at a constant speed as in the usual Minkowski space-time, which implies that an arrival time analysis by γ-rays from Markarian (Mk) 421 does not exclude space-time noncommutativity. Based on this observation, we analyze reaction processes in κ-Minkowski space-time which are related to the puzzling detections of extremely highenergy cosmic rays above the Greisen-Zatsepin-Kuzmin cutoff and of high-energy (∼20 TeV) γ-rays from Mk 501. In these analyses, we take into account the ambiguity of the momentum conservation law which can not be determined uniquely from a mathematical viewpoint. We find that peculiar types of momentum conservation law with some length scale of noncommutativity above a critical length scale can explain such puzzling detections. We also obtain stringent constraints on the length scale of noncommutativity and the freedom of momentum conservation law. 95.85.Pw, 98.70.Sa.

Group velocity in noncommutative spacetime

Journal of Cosmology and Astroparticle Physics, 2003

The realization that forthcoming experimental studies, such as the ones planned for the GLAST space telescope, will be sensitive to Planck-scale deviations from Lorentz symmetry has increased interest in noncommutative spacetimes in which this type of effects is expected. We focus here on κ-Minkowski spacetime, a muchstudied example of Lie-algebra noncommutative spacetime, but our analysis appears to be applicable to a more general class of noncommutative spacetimes. A technical controversy which has significant implications for experimental testability is the one concerning the κ-Minkowski relation between group velocity and momentum. A large majority of studies adopted the relation v = dE(p)/dp, where E(p) is the κ-Minkowski dispersion relation, but recently some authors advocated alternative formulas. While in these previous studies the relation between group velocity and momentum was introduced through ad hoc formulas, we rely on a direct analysis of wave propagation in κ-Minkowski. Our results lead conclusively to the relation v = dE(p)/dp. We also show that the previous proposals of alternative velocity/momentum relations implicitly relied on an inconsistent implementation of functional calculus on κ-Minkowski and/or on an inconsistent description of spacetime translations.

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.

Predictions of noncommutative space-time

1994

An unified structure of noncommutative space-time for both gravity and particle physics is presented. This gives possibilities of testing the idea of noncommutative space-time at the currently available energy scale. There are several arguments indicating that noncommutative space-time is visible already at the electroweak scale. This noncommutative space-time predicts the top quark mass m_t \sim 172 GeV, the Higgs mass M_H \sim 241 GeV and the existence of a vector meson and a scalar, which interact universally with the matter.

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.

Non-commutative spacetime in very special relativity

Physics Letters A, 2011

Very Special Relativity (VSR) framework, proposed by Cohen and Glashow [1], demonstrated that a proper subgroup of the Poincaré group, (in particular ISIM(2)), is sufficient to describe the spacetime symmetries of the so far observed physical phenomena. Subsequently a deformation of the latter, DISIM b (2), was suggested by Gibbons, Gomis and Pope [2].

A free particle in noncommutative space-time

Czechoslovak Journal of Physics, 1996

By examining some known wave equations it is shown that the dynamics of a free quantum particle in a slightly noncommutative space-time is equivalent to that of a charged particle moving in a self-generated (weak) electromagnetic field.

TeV scale implications of non commutative space time in laboratory frame with polarized beams

Journal of High Energy Physics, 2011

We analyze e + e − → γγ, e − γ → e − γ and γγ → e + e − processes within the Seiberg-Witten expanded noncommutative scenario using polarized beams. With unpolarized beams the leading order effects of non commutativity starts from second order in non commutative(NC) parameter i.e. O(Θ 2 ), while with polarized beams these corrections appear at first order (O(Θ)) in cross section. The corrections in Compton case can probe the magnetic component( Θ B ) while in Pair production and Pair annihilation probe the electric component( Θ E ) of NC parameter. We include the effects of earth rotation in our analysis. This study is done by investigating the effects of non commutativity on different time averaged cross section observables. The results which also depends on the position of the collider, can provide clear and distinct signatures of the model testable at the International Linear Collider(ILC).