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Subir Ghosh

Publications and source records attributed to Subir Ghosh.

At least 91 records · Page 5Linked to original sources
arXiv2009

Dirac Quantization Condition for Monopole in Noncommutative Space-Time

Since the structure of space-time at very short distances is believed to get modified possibly due to noncommutativity effects and as the Dirac Quantization Condition (DQC), $μe = \frac{N}{2}\hbar c$, probes the magnetic field point singularity, a natural question arises whether the same condition will still survive. We show that the DQC on a noncommutative space in a model of dynamical noncommutative quantum mechanics remains the same as in the commutative case to first order in the noncommutativity parameter $θ$, leading to the conjecture that the condition will not alter in higher orders.

hep-th↗
arXiv2009

Classical oscillator with position-dependent mass in a complex domain

We study complexified Harmonic Oscillator with a position-dependent mass, termed as Complex Exotic Oscillator (CEO). The complexification induces a gauge invariance [19,11]. The role of PT -symmetry is discussed from the perspective of classical trajectories of CEO for real energy. Some trajectories of CEO are similar to those for the particle in a quartic potential in the complex domain [10, 32].

math-ph↗
arXiv2008

Berry Curvature in Graphene: A New Approach

In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an \textit{inhomogeneous} lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us \cite{ber0,ber1,ber2}. We show that a non-constant lattice distortion leads to a valley-orbit coupling which is responsible to a valley-Hall effect. This is similar to the valley-Hall effect induced by an electric field proposed in \cite{niu2} and is the analogue of the spin-Hall effect in semiconductors \cite{MURAKAMI, SINOVA}. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results \cite{niu2}. We also discuss the Berry phase in the quantization of cyclotron motion.

cond-mat.mes-hall↗
arXiv2008

Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects

We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga \cite{sm} who initiated the study of these Crypto-gauge invariant models that can be related to $PT$-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints, (in contrast to \cite{sm} where one deals with a single constraint), with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator.

hep-th↗
arXiv2008

Comment on Magnetic Monopole Excitations in Spin Ice

It has been proposed recently \cite{son} that excitations in Spin Ice can be of the form of magnetic monopoles that does not obey the Dirac Quantization Condition. It is also well known \cite{rj} that the above scenario leads to non-associativity among translation generators. It will be interesting to see how the monopole picture in Spin Ice survives in the light of the latter observation.

cond-mat.str-el↗
arXiv2007

Three dimensional noncommutative bosonization

We consider the extension of the 2+1-dimensional bosonization process in Non-Commutative (NC) spacetime. We show that the large mass limit of the effective action obtained by integrating out the fermionic fields in NC spacetime leads to the NC Chern-Simons action. The present result is valid to all orders in the noncommutative parameter $θ$. We also discuss how the NC Yang-Mills action is induced in the next to leading order.

hep-th↗
arXiv2007

Spin Hall Effect For Anyons

We explain the intrinsic spin Hall effect from generic anyon dynamics in the presence of external electromagnetic field. The free anyon is represented as a spinning particle with an underlying non-commutative configuration space. The Berry curvature plays a major role in the analysis.

cond-mat.mes-hall↗
arXiv2007

Deformed Special Relativity and Deformed Symmetries in a Canonical Framework

In this paper we have studied the nature of kinematical and dynamical laws in $κ$-Minkowski spacetime from a new perspective: the canonical phase space approach. We discuss a particular form of $κ$-Minkowski phase space algebra that yields the $κ$-extended finite Lorentz transformations derived in \cite{kim}. This is a particular form of a Deformed Special Relativity model that admits a modified energy-momentum dispersion law as well as noncommutative $κ$-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and {\it{not}} $κ$-Minkowski) phase space algebra and Special Relativity Lorentz transformation (and {\it{not}} $κ$-extended Lorentz transformation). The complete set of deformed symmetry generators are constructed that obeys an unmodified closed algebra but induce deformations in the symmetry transformations of the physical $κ$-Minkowski phase space variables. Furthermore, we demonstrate the usefulness and simplicity of this approach through a number of phenomenological applications both in classical and quantum mechanics. We also construct a Lagrangian for the $κ$-particle.

hep-th↗
arXiv2007

DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis

In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. At the same time, the symplectic structure induces a Non-Commutative phase space, which interpolates between $κ$-Minkowski and Snyder phase space. Hence this model bridges an existing gap between two conceptually distinct ideas in a natural way. We thoroughly discuss how this type of construction can be carried out from a phase space (or first order) Lagrangian approach. The inclusion of external physical interactions are also briefly outlined. The work serves as a demonstration of how Hamiltonian (and Lagrangian) dynamics can be built around a given non-trivial symplectic structure.

hep-th↗
arXiv2006

Remarks on the Generalized Chaplygin Gas

We have developed an action formulation for the Generalized Chaplygin Gas (GCG). The most general form for the nonrelativistic GCG action is derived consistent with the equation of state. We have also discussed a relativistic formulation for GCG by providing a detailed analysis of the Poincare algebra.

gr-qc↗
arXiv2006

Noncommutative Geometry and Geometric Phases

We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space. The Ahranov-Bohm effect has been considered in this form of phase space, with operatorial structures of noncommutativity. Physical significance of our results are also discussed.

hep-th↗
arXiv2006

A Lagrangian for DSR Particle and the Role of Noncommutativity

In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the exact Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we demonstrate how a Non-Commutative phase space is needed to maintain Lorentz invariance for the DSR dispersion relation. Lastly we address the very important issue of velocity of this DSR particle. Exploiting the above Non-commutative phase space algebra in a Hamiltonian framework, we show that the speed of massless particles is $c$ and for massive particles the speed saturates at $c$ when the particle energy reaches the maximum value $κ$, the Planck mass.

hep-th↗
arXiv2006

Chaplygin Gravitodynamics

We consider a new approach for gravity theory coupled to Chaplygin matter in which the {\it{relativistic}} formulation of the latter is of crucial importance. We obtain a novel form of matter with dust like density $(\sim (volume)^{-1})$ and negative pressure. We explicitly show that our results are compatible with a relativistic generalization of the energy conservation principle, derived here.

gr-qc↗
arXiv2006

Study of the "Non-Abelian" Current Algebra of a Non-linear $σ$-Model

A particular form of non-linear $σ$-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-abelian nature of the invariance, with {\it{field dependent structure functions}}. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in \cite{car}. The connection with noncommutative geometry is also established.

hep-th↗
arXiv2006

A Novel "Magnetic" Field And Its Dual Non-Commutative Phase Space

In this paper we have studied a new form of Non-Commutative (NC) phase space with an operatorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an "{\it{internal}}" magnetic field, that is singular at a specific position $θ^{-1}$. By "internal" we mean that the effective magnetic fields depends essentially on the particle properties and modifies the symplectic structure. Here $θ$ is the NC parameter and induces the coupling between the particle and the "internal" magnetic field. The magnetic moment of the particle is computed. Interaction with an {\it{external}} physical magnetic field reveals interesting features induced by the inherent fuzziness of the NC phase space: introduction of non-trivial structures into the charge and mass of the particle and possibility of the particle dynamics collapsing to a Hall type of motion. The dynamics is studied both from Lagrangian and symplectic (Hamiltonian) points of view. The canonical (Darboux) variables are also identified. We briefly comment, that the model presented here, can play interesting role in the context of (recently observed) {\it{real}} space Berry curvature in material systems.

hep-th↗
arXiv2005

Lie Particle And Its Batalin-Tyutin Extension

In this Letter we have proposed a point particle model that generates a noncommutative three-space, with the coordinate brackets being Lie algebraic in nature, in particular isomorphic to the angular momentum algebra. The work is in the spirit of our earlier works in this connection, {\it {i.e.}} PLB 618 (2005)243 and PLB 623 (2005)251, where the $κ$-Minkowski form of noncomutative spacetime was considered. This non-linear and operatorial nature of the configuration space coordinate algebra can pose problems regarding its quantization. This prompts us to embed the model in the Batalin-Tyutin extended space where the equivalent model comprises of phase space variables satisfying a canonical algebra. We also compare our present model with the point particle model, previously proposed by us, in the context of $κ$-Minkowski spacetime.

hep-th↗