arXiv subjects

Subir Ghosh

Publications and source records attributed to Subir Ghosh.

At least 73 records · Page 4Linked to original sources

arXiv2012

"Stringy" Coherent States Inspired By Generalized Uncertainty Principle

In this Letter we have explicitly constructed Generalized Coherent States for the Non-Commutative Harmonic Oscillator that directly satisfy the Generalized Uncertainty Principle (GUP). Our results have a smooth commutative limit. The states show fractional revival which provides an independent bound on the GUP parameter. Using this and similar bounds we derive the largest possible value of the (GUP induced) minimum length scale. Mandel parameter analysis shows that the statistics is Sub-Poissionian.

hep-th↗

arXiv2011

Coherent States for the Non-Linear Harmonic Oscillator

Wave packets for the Quantum Non-Linear Oscillator are considered in the Generalized Coherent State framerwork. To first order in the non-linearity parameter the Coherent State behaves very similarly to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features, (such as the Squeezed State nature), of the Coherent State have been discussed.

quant-ph↗

arXiv2011

Gauge Invariant Extension of Linearized Horava Gravity

In the present paper we have constructed a gauge invariant extension of a generic Horava Gravity (HG) model (with quadratic curvature terms) in linearized version in a systematic procedure. No additional fields are introduced. The linearized HG model is explicitly shown to be a gauge fixed version of the Einstein Gravity (EG) thus proving the Bellorin-Restuccia conjecture in a robust way. In the process we have explicitly computed the correct Hamiltonian dynamics using Dirac Brackets appearing from the Second Class Constraints present in the HG model. We comment on applying this scheme to the full non-linear HG.

gr-qc↗

arXiv2011

Constrained Dynamics of an Anomalous $(g/neq 2)$ Relativistic Spinning Particle in Electromagnetic Background

In this paper we have considered the dynamics of an anomalous ($g\neq 2$) charged relativistic spinning particle in the presence of an external electromagnetic field. The constraint analysis is done and the complete set of Dirac brackets are provided that generate the canonical Lorentz algebra and dynamics through Hamiltonian equations of motion. The spin-induced effective curvature of spacetime and its possible connection with Analogue Gravity models are commented upon.

hep-th↗

arXiv2011

Spontaneous Symmetry Breaking and Landau Phase Transition in Horava Gravity

Presence of higher derivative terms in the Horava model of gravity can generate an instability in the Minkowski ground state. This in turn leads to a space dependent vacuum metric with a length scale determined by the higher derivative coupling coefficient. The translation invariance is spontaneously broken in the process. The phenomenon is interpreted as a form of Landau liquid-solid phase translation. The (metric) condensate acts as a source that modifies the Newtonian potential below the length scale but keeps it unchanged for sufficiently large distance.

hep-th↗

arXiv2011

Noncommutative Spacetime in Very Special Relativity

Very Special Relativity (VSR) framework, proposed by Cohen and Glashow [1], demonstrated that a proper subgroup of the Poincaré group, (in particular ISIM(2)), is sufficient to describe the spacetime symmetries of the so far observed physical phenomena. Subsequently a deformation of the latter, $DISIM_b(2)$, was suggested by Gibbons, Gomis and Pope [2]. In the present work, we introduce a novel Non-Commutative (NC) spacetime structure, underlying the $DISIM_b(2)$. This allows us to construct explicitly the $DISIM_b(2)$ generators, consisting of a sector of Lorentz rotation generators and the translation generators. Exploiting the Darboux map technique, we construct a point particle Lagrangian that lives in the NC phase space proposed by us and satisfies the modified dispersion relation proposed by Gibbons et. al. [2]. It is interesting to note that in our formulation the momentum algebra becomes non-commutative.

hep-th↗

arXiv2011

Black Hole Entropy: From Shannon to Bekenstein

In this note we have applied directly the Shannon formula for information theory entropy to derive the Black Hole (Bekenstein-Hawking) entropy. Our analysis is semi-classical in nature since we use the (recently proposed [8]) quantum mechanical near horizon mode functions to compute the tunneling probability that goes in to the Shannon formula, following the general idea of [5]. Our framework conforms to the information theoretic origin of Black Hole entropy, as originally proposed by Bekenstein.

hep-th↗

arXiv2011

Generalized particle dynamics in anti de Sitter spaces: A source for dark energy

We consider the generalized particle dynamics, proposed by us, in brane world formalisms for an asymptotically anti de Sitter background. The present framework results in a new model that accounts for the late acceleration of the universe. An effective Dark Energy equation of state, exhibiting a phantom like behaviour, is generated. The model is derived by embedding the physical FRW universe in a $(4+1)$-dimensional effective space-time, induced by the generalized particle dynamics. We corroborate our results with present day observed cosmological parameters.

astro-ph.CO↗

arXiv2011

Quantum mechanics in de Sitter space

We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.

hep-th↗

arXiv2011

Planck Scale Effect in the Entropic Force Law

In this note we generalize the quantum uncertainty relation proposed by Vancea and Santos [7] in the entropic force law, by introducing Planck scale modifications. The latter is induced by the Generalized Uncertainty Principle. We show that the proposed uncertainty relation of [7], involving the entropic force and the square of particle position, gets modified from the consideration of a minimum measurable length, (which can be the Planck length).

hep-th↗

arXiv2010

Towards a Discrete Spacetime

A formalism is proposed to generate (the first step of) a discrete spacetime: spacetime with an inbuilt length scale. We follow the celebrated Landau theory of liquid - solid phase transition induced by Spontaneous Symmetry Breaking by a condensate whose Fourier transform has support at a {\it{non-zero}} momentum. The latter requirement is essential for breaking the translation symmetry. This, in turn, compels us to generalize Einstein action to higher derivative terms.

hep-th↗

arXiv2009

Relativistic Thermodynamics with an Invariant Energy Scale

A particular framework for Quantum Gravity is the Doubly Special Relativity (DSR) formalism that introduces a new observer independent scale, the Planck energy. Our aim in this paper is to study the effects of this energy upper bound in relativistic thermodynamics. We have explicitly computed the modified equation of state for an ideal fluid in the DSR framework. In deriving our result we exploited the scheme of treating DSR as a non-linear representation of the Lorentz group in Special Relativity.

hep-th↗

arXiv2009

The E(2) Particle

Recently it has been advocated [1] that for describing nature within the minimal symmetry requirement, certain subgroups of Lorentz group may play a fundamental role. One such group is E(2) which induces a Lie algebraic Non-Commutative spacetime [4] where translation invariance is not fully maintained. We have constructed a consistent structure of Non-commutative phase space for this system and furthermore we have studied an appropriate point particle action on it. Interestingly, the Einstein dispersion relation $p^2=m^2$ remains intact. The model is constructed by exploiting a dual canonical phase space following the scheme developed by us earlier [8].

hep-th↗

arXiv2009

Relativistic Spinning Particle in a Non-Commutative Extended Spacetime

The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily constrained and constraint analysis, in the Dirac scheme, is both novel and instructive. Our major finding is an associated novel non-commutative structure in the extended space. This is obtained in a particular gauge. The model possesses a large gauge freedom and hence a judicious choice of gauge becomes imperative. The gauge fixed system in reduced phase space simplifies considerably for further study. We have shown that this non-commutative phase space algebra is essential in revealing the spin effects in the particle model through the Lorentz generator and Hamiltonian equations of motion.

hep-th↗

arXiv2009

Topics in Noncommutative Geometry Inspired Physics

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.

hep-th↗

arXiv2009

Spectral Discontinuities in Constrained Dynamical Models

As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint analysis of Dirac [1] and find that the nature of constraints depends critically on a $c$-number parameter present in the model. Thus a change in the parameter alters the number of dynamical modes in an abrupt and non-perturbative way. We have obtained new {\it{real}} energy levels for the quantum mechanical model as we explore {\it{complex}} domains in the parameter space. These were forbidden in the parent chiral Schwinger field theory where the analogue Jackiw-Rajaraman parameter is restricted to be real. We explicitly show existence of modes that satisfy higher derivative Pais-Uhlenbeck form of dynamics [3]. We also show that the Cranking Model [7], well known in Nuclear Physics, can be interpreted as a spatially frozen version of another well studied relativistic field theory in 2+1-dimension- the Maxwell-Chern-Simons-Proca Model [8].

math-ph↗

arXiv2009

Combining The Tunneling And Anomaly Phenomena In Deriving the Gravitational Anomaly

In this Letter we have derived the gravitational anomaly leading to the Hawking radiation from a fundamentally different perspective: it emerges due to the {\it{complimentary}} roles played by tunneling and (gravitational) anomaly. We have used the analogy of an early idea \cite{niel1} of visualizing chiral gauge anomaly as an effect of {\it{spectral flow}} of the energy levels, from the negative energy Dirac sea, across zero energy level in presence of gauge interactions. This was extended to conformal anomaly in \cite{fumita}. In the present work, we exploit the latter formalism in black hole physics where we interpret crossing the horizon of black hole (the zero energy level) as a spectral flow since it is also accompanied by a change of sign in the energy of the particle. Hence in our formulation the negative energy states below horizon play a similar role as the Dirac sea. We successfully recover the gravitational anomaly.

hep-th↗

arXiv2009

Generalized particle dynamics: modifying the motion of particles and branes

We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this generalized dynamics to the motion of test particles in a static, spherically symmetric metric. A significant consequence of the new framework is to generate an effective negative pressure on a cosmological surface whose expansion is manifest by the particle trajectory via embedding geometry \cite{bwg,embed2,embed,pal}. This formalism thus may give rise to a source for dark energy in modeling the late accelerating universe.

gr-qc↗