• DOI:10.1103/PhysRevD.75.105021
• Corpus ID: 17769630

Deformed special relativity and deformed symmetries in a canonical framework

@article{Ghosh2007DeformedSR,
  title={Deformed special relativity and deformed symmetries in a canonical framework},
  author={Subir Kumar Ghosh and Probir Pal},
  journal={Physical Review D},
  year={2007},
  volume={75},
  pages={105021}
}

• S. Ghosh, Probir Pal
• Published 20 February 2007
• Mathematics
• Physical Review D

In this paper we have studied the nature of kinematical and dynamical laws in $\ensuremath{\kappa}$-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of $\ensuremath{\kappa}$-Minkowski phase space algebra that yields the $\ensuremath{\kappa}$-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 $\ensuremath{\kappa}$-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and not $\ensuremath{\kappa}$-Minkowski) phase space algebra and special relativity Lorentz transformation (and not $\ensuremath{\kappa}$-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 $\ensuremath{\kappa}$-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 $\ensuremath{\kappa}$-particle.