# Path integral action of a particle in κ-Minkowski spacetime

@article{Verma2018PathIA, title={Path integral action of a particle in $\kappa$-Minkowski spacetime}, author={Ravikant Verma and Debabrata Ghorai and Sunandan Gangopadhyay}, journal={Europhysics Letters}, year={2018}, volume={122} }

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…

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## References

SHOWING 1-10 OF 16 REFERENCES

### Classical and Quantum Mechanics of Free κ-Relativistic Systems

- Physics
- 1993

We consider the Hamiltonian and Lagrangian formalism describing free κ-relativistic particles with their four-momenta constrained to the κ-deformed mass shell. We study the formalism with commuting…

### Path-integral action of a particle in the noncommutative plane.

- Physics, MathematicsPhysical review letters
- 2009

A coherent state approach to the path-integral representation of the transition amplitude of the free particle and harmonic oscillator is formulated and it is found that this action is nonlocal in time.

### Path integral action of a particle in a magnetic field in the noncommutative plane and the Aharonov–Bohm effect

- Physics
- 2014

The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert–Schmidt operators is used to systematically derive, using the standard time slicing…

### κ-Minkowski spacetime and the star product realizations

- Mathematics
- 2008

We investigate a Lie algebra-type κ-deformed Minkowski spacetime with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of…

### Quantum symmetry, the cosmological constant and Planck scale phenomenology

- Physics
- 2003

We present a simple algebraic mechanism for the emergence of deformations of Poincar? symmetries in the low-energy limit of quantum theories of gravity. The deformations, called ?-Poincar? algebras,…

### Quantum Symmetry

- Mathematics
- 1993

The representations of the observable algebra of a low dimensional quantum ﬁeld theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to ﬁnding an…

### Feynman Path Integral on the Noncommutative Plane

- Physics, Mathematics
- 2003

. We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-oﬀ induced by the parameter of non commutativity.

### Quantum Field Theory

- PhysicsCompendium of Quantum Physics
- 2009

Quantum field theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the standard model, are formulated. Quantum electrodynamics (QED),…