this paper, we study the effect of deformation of the space-time on the response function of a uniformly accelerating detector coupled to a scalar field. Starting with -deformed Klein-Gordon theory, which is invariant under a -Poincaré algebra and written in commutative space-time, we derive -deformed Wightman functions, valid up to second order in the deformation parameter a. Using this, we show that the first nonvanishing correction to the Unruh thermal distribution is only in the second order in a. We also discuss various other possible sources of a-dependent corrections to this thermal distribution.
In this paper, we investigate how a uniformly accelerated detector responds to vacuum state of a Dirac field in the κ-Minkowski spacetime. Starting from κ-deformed Dirac theory, which is invariant under κ-Poincare algebra, we derive κ-deformed Wightmann function for Dirac field, which is valid up to first order in the deformation parameter a. Using this, we calculate the response function of the uniformaly accelerated detector, which is coupled to massless Dirac field in κspacetime. From this, we obtain the modification to Unruh effect for the κ-deformed Dirac field, valid up to first order in the deformation parameter. *
In this paper, we investigate the twisted algebra of the fermionic oscillators associated with Dirac field defined in κ-Minkowski spacetime. Starting from κ-deformed Dirac theory, which is invariant under the undeformed κ-Poincare algebra, using the twisted flip operator, we derive the deformed algebra of the creation and annihilation operators corresponding to the Dirac field quanta in κ-Minkowski space-time. In the limit a →0, the deformed algebra reduces to the commutative result. *
In this paper, we present the results of our investigation on the modification of Zitterbewegung due to the noncommutativity of the space-time. First, we study the effect of κ-deformation of the spacetime on Zitterbewegung. For this, we start with the κ-deformed Dirac theory and using κ-deformed Dirac equation valid upto first order in deformation parameter a, we find the modification in the Zitterbewegung valid upto first order in the deformation parameter a. In the limit a → 0, we get back the commutative result. Secondly, we find the modification in the Zitterbewegung due to the Magueijo-Smolin(MS) approach of doubly special relativity(DSR) and in the limit E p → ∞, we get back the result in the commutative space-time.
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 operator approach upto 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, a → 0, the commutative results are recovered.
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