1993/12/17 by J. Lukierski, H. Ruegg, W. J. Zakrzewski · 9 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Electron #Energy (signal processing) #Energy operator #Formalism (music) #Hamiltonian (control theory) #Physics #Poisson bracket #Quantum #Quantum Mechanics and Applications #Quantum dissipation #Quantum mechanics #Quantum statistical mechanics #Relativistic mechanics #Relativistic particle #Relativistic quantum chemistry #Relativistic quantum mechanics #Statistical Mechanics and Entropy #Theory of relativity #advanced mathematical theories #hep-th
paper · pdf · doi:10.1006/aphy.1995.1092
published as Ann.Phys.243:90-116,1995 · 27 pages, DTP-57/93
arxiv created 1993/12/17 · openalex publication_date 1995/10/01 · arxiv updated 2011/05/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 Schrödinger quantum mechanics in which the time derivative is replaced by a finite difference derivative is also discussed.