Path integral action of a particle in κMinkowski spacetime
Abstract
In this letter, we derive the path integral action of a particle in κMinkowski spacetime. The equation of motion for an arbitrary potential due to the κdeformation of the Minkowski spacetime is then obtained. The action contains a dissipative term which owes its origin to the κMinkowski deformation parameter a. We take the example of the harmonic oscillator and obtain the frequency of oscillations in the path integral approach as well as the operator approach up to the first order in the deformation parameter a. For studying this, we start with the κdeformed dispersion relation which is invariant under the undeformed κPoincaré algebra and take the nonrelativistic limit of the κdeformed dispersion relation to find the Hamiltonian. The propagator for the free particle in the κMinkowski spacetime is also computed explicitly. In the limit, a→ 0 , the commutative results are recovered.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 May 2018
 DOI:
 10.1209/02955075/122/40001
 arXiv:
 arXiv:1802.00720
 Bibcode:
 2018EL....12240001V
 Keywords:

 Physics  General Physics;
 High Energy Physics  Theory
 EPrint:
 5 pages, To appear in Euro.Phys. Lett