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.
Classical and Quantum Mechanics of Free \k Relativistic Systems
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abstract
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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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.
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Kinematical correlations via $\kappa$-Poincar\'e coproducts
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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Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes
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.