arXiv subjects

E. Harikumar

Publications and source records attributed to E. Harikumar.

At least 37 records · Page 2Linked to original sources

arXiv2020

Maximal acceleration in non-commutative space-time and its implications

In this paper, we derive the non-commutative corrections to the maximal acceleration of a massive particle. Using the eight-dimensional kappa-deformed phase-space metric, we obtain the kappa-deformed maximal acceleration, valid up to first order in the deformation parameter. We then derive the kappa-deformed geodesic equation and obtain its Newtonian limit and from this obtain a bound on the deformation parameter. After re-expressing the kappa-deformed Schwarzschild metric in terms of maximal acceleration, we analyse the motion of a particle in this space-time, and also study the modifications to Hawking radiation. We also derive the kappa-deformed corrections to maximal acceleration using kappa-deformed generalised uncertainty principle.

hep-th↗

arXiv2020

Quantisation of $κ$-deformed Dirac equation

In this paper, we study the quantisation of Dirac field theory in the $κ$-deformed space-time. We adopt a quantisation method that uses only equations of motion for quantising the field. Starting from $κ$-deformed Dirac equation, valid up to first order in the deformation parameter $a$, we derive deformed unequal time anti-commutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anti-commutation relations between $κ$-deformed spinor and its adjoint, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the $κ$-deformed conserved currents, valid up to first order in $a$, corresponding to parity and time-reversal symmetries of $κ$-deformed Dirac equation also. We show that these conserved currents and charges have a mass-dependent correction, valid up to first order in $a$. This novel feature is expected to have experimental significance in particle physics. We also show that it is not possible to construct a conserved current associated with charge conjugation, showing that the Dirac particle and its anti-particle satisfy different equations in $κ$-space-time.

hep-th↗

arXiv2019

Time-space noncommutativity and Casimir effect

We show that the Casimir force and energy are modified in the kappa-deformed space-time. This is analysed by solving the Green's function corresponding to kappa-deformed scalar field equation in presence of two parallel plates, modelled by delta-function potentials. Exploiting the relation between energy-momentum tensor and Green's function, we calculate the correction to Casimir force, valid up to second order in the deformation parameter. The Casimir force is shown to get corrections which scale as $L^{-4}$ and $L^{-6}$ and both these types of corrections produce attractive forces. Using the measured value of Casimir force, we show that the deformation parameter should be below $10^{-23}$m.

hep-th↗

arXiv2019

Quantisation of Klein-Gordon field in $κ$ space-time: deformed oscillators and Unruh effect

In this paper we study the quantisation of scalar field theory in $κ$-deformed space-time. Using a quantisation scheme that use only field equations, we derive the quantisation rules for deformed scalar theory, starting from the $κ$-deformed equations of motion. This scheme allows two choices; (i)a deformed commutation relation between the field and its conjugate which leads to usual oscillator algebra, (ii) an undeformed commutation relation between field and its conjugate leading to a deformed oscillator algebra. This deformed oscillator algebra is used to derive modification to Unruh effect in the $κ$-space-time.

hep-th↗

arXiv2019

Superdense star in a space-time with minimal length

In this paper we generalise core-envelope model of superdense star to a non-commutative space-time and study the modifications due to the existence of a minimal length, predicted by various approaches to quantum gravity. We first derive Einstein's field equation in $κ$-deformed space-time and use this to set up non-commutative version of core-envelope model describing superdense stars. We derive $κ$-deformed law of density variation, valid up to first order approximation in deformation parameter and obtain radial and tangential pressures in $κ$-deformed space-time. We also derive $κ$-deformed strong energy conditions and obtain a bound on the deformation parameter.

gr-qc↗

arXiv2017

Non-Commutative space-time and Hausdorff dimension

We study the Hausdorff dimension of the path of a quantum particle in non-commutative space-time. We show that the Hausdorff dimension depends on the deformation parameter $a$ and the resolution $Δx$ for both non-relativistic and relativistic quantum particle. For the non-relativistic case, it is seen that Hausdorff dimension is always less than two in the non-commutative space-time. For relativistic quantum particle, we find the Hausdorff dimension increases with the non-commutative parameter, in contrast to the commutative space-time. We show that non-commutative correction to Dirac equation brings in the spinorial nature of the relativistic wave function into play, unlike in the commutative space-time. By imposing self-similarity condition on the path of non-relativistic and relativistic quantum particle in non-commutative space-time, we derive the corresponding generalised uncertainty relation.

hep-th↗

arXiv2017

Conformal quantum mechanics and holography in noncommutative space-time

We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the $κ$-deformed space-time as a prototype. Upto the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The $AdS_2/CFT_1$ duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.

hep-th↗

arXiv2017

Compact stars in quantum spacetime

We derive bounds on the deformation parameter of the $κ$-spacetime by analyzing the effect of non-commutativity on astrophysical model. We study compact stars, taken to be degenerate Fermi gas, in non-commutative spacetime. Using tools of statistical mechanics, we derive the degeneracy pressure of the compact star in $κ$-spacetime and from the hydrostatic equilibrium conditions we obtain a bound on the deformation parameter. We independently derive this bound using generalized uncertainty principle, which is a characteristic feature of quantum gravity approaches, strengthening the bound obtained.

hep-th↗

arXiv2017

Hawking radiation in the kappa-spacetime

In this paper, we analyze the Hawking radiation of a kappa-deformed Schwarzchild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the kappa-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzchild metric obtained in the kappa-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1+1 dimensions, to solve the kappa-deformed Klein-Gordon equation in the background of the Schwarzchild metric. The method of Boguliobov coefficients is then used to calculate the thermal spectrum of kappa-deformed-Schwarzchild black hole and show that the Hawking temperature is modified by the non-commutativity of the kappa-spacetime.

hep-th↗

arXiv2016

Regularization of Kepler Problem in $κ$-spacetime

In this paper we regularize the Kepler problem on $κ$-spacetime in several different ways. First, we perform a Moser-type regularization and then we proceed for the Ligon-Schaaf regularization to our problem. In particular, generalizing Heckman-de Laat (J. Symplectic Geom. 10, (2012), 463-473) in the noncommutative context we show that the Ligon-Schaaf regularization map follows from an adaptation of the Moser regularization can be generalized to the Kepler problem on $κ$-spacetime.

math-ph↗

arXiv2015

Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole

We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for quasinormal mode frequencies, the area and entropy spectra for the BTZ black hole in the presence of noncommutativity are calculated. In particular, the separations between the neighboring values of these spectra are determined and it is found that they are nonuniform. Therefore, it appears that the noncommutativity leads to a non-equispaced (discrete) area and entropy spectra.

hep-th↗

arXiv2015

Dimensional flow in the kappa-deformed space-time

We derive the modified diffusion equations defined on kappa-space-time and using these, investigate the change in the spectral dimension of kappa-space-time with the probe scale. These deformed diffusion equations are derived by applying Wick's rotation to the $κ$-deformed Schr$\ddot{o}$dinger equations obtained from different choices of Klein-Gordon equations in the $κ$-deformed space-time. Using the solutions of these equations, obtained by perturbative method, we calculate the spectral dimension for different choices of the generalized Laplacian and analyse the dimensional flow in the $κ$-space-time. In the limit of commutative space-time, we recover the well known equality of spectral dimension and topological dimension. We show that the higher derivative term in the deformed diffusion equations make the spectral dimension unbounded (from below) at high energies. We show that the finite mass of the probe results in the spectral dimension to become infinitely negative at low energies also. In all the cases, we have analysed the effect of finite size of the probe on the spectral dimension.

hep-th↗

arXiv2015

Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time

We study presence of an additional symmetry of a generic central potential in the $κ$-space-time. An explicit construction of Fradkin and Bacry, Ruegg, Souriau (FBRS) for a central potential is carried out and the piece-wise conserved nature of the vector is established. We also extend the study to Kepler systems with a drag term, particularly Gorringe-Leach equation is generalized to the $κ$-deformed space. The possibility of mapping Gorringe-Leach equation to an equation with out drag term is exploited in associating a similar conserved vector to system with a drag term. An extension of duality between two class of central potential is introduced in the $κ$-deformed space and is used to investigate the duality existing between two class of Gorringe-Leach equations. All the results obtained can be retraced to the correct commutative limit as we let $a \rightarrow 0$.

hep-th↗

arXiv2015

Spectral Dimension of kappa-deformed space-time

We investigate the spectral dimension of $κ$-space-time using the $κ$-deformed diffusion equation. The deformed equation is constructed for two different choices of Laplacians in $n$-dimensional, $κ$-deformed Euclidean space-time. We use an approach where the deformed Laplacians are expressed in the commutative space-time itself. Using the perturbative solutions to diffusion equations, we calculate the spectral dimension of $κ$-deformed space-time and show that it decreases as the probe length decreases. By introducing a bound on the deformation parameter, spectral dimension is guaranteed to be positive definite. We find that, for one of the choices of the Laplacian, the non-commutative correction to the spectral dimension depends on the topological dimension of the space-time whereas for the other, it is independent of the topological dimension. We have also analysed the dimensional flow for the case where the probe particle has a finite extension, unlike a point particle.

hep-th↗

arXiv2014

Effects of Noncommutativity on the Black Hole Entropy

In this paper the BTZ black hole geometry is probed with a noncommutative scalar field which obeys the $κ$-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton's constant due to the effects of the noncommutativity.

hep-th↗

arXiv2014

MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws

In this paper, we analyze the modification of integrable models in the $κ$-deformed space-time. We show that two dimensional isotropic oscillator problem, Kepler problem and MICZ-Kepler problem in $κ$-deformed space-time admit integrals of motion as in the commutative space. We also show that the duality equivalence between $κ$-deformed Kepler problem and $κ$-deformed two-dimensional isotropic oscillator explicitly, by deriving Bohlin-Sundman transformation which maps these two systems. These results are valid to all orders the the deformation parameter.

hep-th↗

arXiv2013

Uniformly accelerated detector in the $κ$-deformed Dirac vacuum

In this paper, we investigate how a uniformly accelerated detector responds to vacuum state of a Dirac field in the $κ$-Minkowski space-time. 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 uniformly accelerated detector, which is coupled to massless Dirac field in $κ$-spacetime. From this, we obtain the modification to Unruh effect for the $κ$-deformed Dirac field, valid up to first order in the deformation parameter.

hep-th↗

arXiv2013

A Dirac type xp-Model and the Riemann Zeros

We propose a Dirac type modification of the xp-model to a $x \slashed{p}$ model on a semi-infinite cylinder. This model is inspired by recent work by Sierra et al on the xp-model on the half-line. Our model realizes the Berry-Keating conjecture on the Riemann zeros. We indicate the connection of our model to that of gapped graphene with a supercritical Coulomb charge, which might provide a physical system for the study of the zeros of the Riemann Zeta function.

math-ph↗