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Classical and Quantum Mechanics of Free \k Relativistic Systems

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arxiv hep-th/9312153 v1 pith:5WMSKTQ5 submitted 1993-12-17 hep-th

J. Lukierski , H. Ruegg , W.J. Zakrzewski This is my paper · ORCID
classification hep-th
keywords freek-relativisticquantummechanicsderivativefiniteformalismk-deformed
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We consider the Hamiltonian and Lagrangian formalism describing free \k-relativistic particles with their four-momenta constrained to the \k-deformed mass shell. We study the modifications of the formalism which follow from the introduction of space coordinates with nonvanishing Poisson brackets and from the redefinitions of the energy operator. The quantum mechanics of free \k-relativistic particles and of the free \k-relativistic oscillator is also presented. It is shown that the \k-relativistic oscillator describes a quantum statistical ensemble with finite Hagedorn temperature. The relation to a \k-deformed Schr\"odinger quantum mechanics in which the time derivative is replaced by a finite difference derivative is also discussed.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Minimal covariant quantum space-time

    hep-th 2025-02 conditional novelty 6.0 of 10

    The minimal covariant quantum space-time M^{1,3}_0 is shown to be a quantized twistor space, an S2 bundle over a k=-1 FLRW space-time, with localized quasi-coherent states.

  2. Kinematical correlations via $\kappa$-Poincar\'e coproducts

    hep-th 2026-06 unverdicted novelty 5.0 of 10

    In the classical basis the non-bijective momentum map induces branch-dependent κ-deformed back-to-back correlations for two-particle states obeying vanishing total momentum.

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