2007/02/28 by Subir Ghosh, Probir Pal · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Geometry #Homogeneous space #Lorentz covariance #Lorentz group #Lorentz transformation #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Phase space #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Special relativity #Symmetry (geometry) #Theoretical physics #Theory of relativity #astro-ph #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.75.105021
published as Phys.Rev.D75:105021,2007 · Revised version with change in Title and Abstract, No change in mathematical content, Reference section enlarged, Discussion on Soccer Ball Problem removed; Version to appear in PRD
arxiv created 2007/05/04 · openalex publication_date 2007/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we have studied the nature of kinematical and dynamical laws in \ensuremathκ-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of \ensuremathκ-Minkowski phase space algebra that yields the \ensuremathκ-extended finite Lorentz transformations derived in [D. Kimberly, J. Magueijo, and J. Medeiros, Phys. Rev. D 70, 084007 (2004).]. This is a particular form of a deformed special relativity model that admits a modified energy-momentum dispersion law as well as noncommutative \ensuremathκ-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not \ensuremathκ-Minkowski) phase space algebra and special relativity Lorentz transformation (and not \ensuremathκ-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical \ensuremathκ-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the \ensuremathκ-particle.