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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

Classical and Quantum Mechanics of Free k Relativistic Systems

J. Lukierski , H. Ruegg , W.J. Zakrzewski This is my paper
classification hep-th
keywords freek-relativisticquantummechanicsderivativefiniteformalismk-deformed
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 3 Pith papers

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

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

    hep-th 2026-06 unverdicted novelty 5.0

    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.

  2. Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes

    gr-qc 2026-04 unverdicted novelty 5.0

    κ-deformation induces critical behavior and phase transitions in uncharged Schwarzschild-AdS black holes with Pc vc/Tc ≈ 0.37 independent of κ and a double-loop G-T structure.

  3. Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes

    gr-qc 2026-04 unverdicted novelty 5.0

    κ-deformation of Schwarzschild-AdS induces critical behaviour with P_c v_c/T_c ≃ 0.370, independent of the deformation parameter and near the Van der Waals ratio.