Souvik Pramanik

Path integral quantization corresponding to the deformed Heisenberg algebra

Abstract In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.

GUP-BASED AND SNYDER NONCOMMUTATIVE ALGEBRAS, RELATIVISTIC PARTICLE MODELS, DEFORMED SYMMETRIES AND INTERACTION: A UNIFIED APPROACH

We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincare generators for the systems that keep space–time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

Electrodynamics of a generalized charged particle in doubly special relativity framework

Abstract In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ -Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ -Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.

Conformal Invariance in Noncommutative Geometry and Mutually Interacting Snyder Particles

A system of relativistic Snyder particles with mutual two-body interaction that lives in a Non-Commutative Snyder geometry is studied. The underlying symplectic structure is a coupled, novel kind and extended version of Snyder algebra. In a recent work by Casalbuoni and Gomis, Phys.Rev. D90, 026001 (2014) [1], a system of interacting conventional particles (in commutative spacetime) was studied with special emphasis on it’s Conformal Invariance. Succeed along the same lines [1] we have shown that our interacting Snyder particle model is also conformally invariant. Moreover the conformal Killing vectors have been constructed. Our main emphasis is on the Hamiltonian analysis of the conformal symmetry generators. We demonstrate that the Lorentz algebra remains undeformed but validity of the full conformal algebra requires further restrictions.

Noncommutative extension of AdS–CFT and holographic superconductors

Abstract In this Letter, we consider a Non-Commutative (NC) extension of AdS–CFT correspondence and its effects on holographic superconductors. NC corrections are incorporated via the NC generalization of Schwarzschild black hole metric in AdS with the probe limit. We study NC effects on the relations connecting the charge density and the critical temperature of the Holographic Superconductors. Furthermore, condensation operator of the superconductor has been analyzed. Our results suggest that generically, NC effects increase the critical temperature of the holographic superconductor.

Scalar field cosmology modified by the generalized uncertainty principle

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter

Implication of the geodesic equation in the generalized uncertainty principle framework

w_{GUP}

Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral

can cross the phantom divide line; that is

ON THE STABILITY OF COHERENT STATES FOR PAIS–UHLENBECK OSCILLATOR

w_{GUP}<-1

Particle on a torus knot: Constrained dynamics and semi-classical quantization in a magnetic field

. Furthermore, we derive the field equations in the dimensionless parameters, the dynamical system which arises is a singular perturbation system in which we study the existence of the fixed points in the slow manifold. Finally, we perform numerical simulations for some well known models and we show that for these models with the specific initial conditions, the parameter