Volume 122, Number 4, May 2018
|Number of page(s)||5|
|Published online||25 June 2018|
Path integral action of a particle in κ-Minkowski spacetime
Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III Salt Lake, Kolkata-700106, India
Received: 1 February 2018
Accepted: 11 June 2018
In this letter, we derive the path integral action of a particle in κ-Minkowski spacetime. The equation of motion for an arbitrary potential due to the κ-deformation of the Minkowski spacetime is then obtained. The action contains a dissipative term which owes its origin to the κ-Minkowski 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 κ-deformed dispersion relation which is invariant under the undeformed κ-Poincaré algebra and take the non-relativistic limit of the κ-deformed dispersion relation to find the Hamiltonian. The propagator for the free particle in the κ-Minkowski spacetime is also computed explicitly. In the limit, , the commutative results are recovered.
PACS: 03.65.-w – Quantum mechanics / 03.65.Ca – Formalism
All authors contributed equally to this work.; email@example.com
© EPLA, 2018
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