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Subir Ghosh

Publications and source records attributed to Subir Ghosh.

At least 109 records · Page 6Linked to original sources
arXiv2005

The $AdS$ particle

In this note we have considered a relativistic Nambu-Goto model for a particle in $AdS$ metric. With appropriate gauge choice to fix the reparameterization invariance, we recover the previously discussed \cite{pal} "Exotic Oscillator". The Snyder algebra and subsequently the $κ$-Minkowski spacetime are also derived. Lastly we comment on the impossibility of constructing a noncommutative spacetime in the context of open string where only a curved target space is introduced.

hep-th↗
arXiv2005

Quantum Hall Effect In Bilayer Systems And The Noncommutative Plane: A Toy Model Approach

We have presented a quantum mechanical toy model for the study of Coulomb interactions in Quantum Hall (QH) system. Inclusion of Coulomb interaction is essential for the study of {\it{bilayer}} QH system and our model can simulate it, in the compound state, in a perturbative framework. We also show that in the noncommutative plane, the Coulomb interaction is modified at a higher order in the noncommutativity parameter $θ$, and only if $θ$ varies from layer to layer in the QH system.

cond-mat.mes-hall↗
arXiv2005

$κ$-Minkowski Spacetime Through Exotic "Oscillator"

We have proposed a generally covariant non-relativistic particle model that can represent the $κ$-Minkowski noncommutative spacetime. The idea is similar in spirit to the noncommutative particle coordinates in the lowest Landau level. Physically our model yields a novel type of dynamical system, (termed here as Exotic "Oscillator"), that obeys a Harmonic Oscillator like equation of motion with a {\it{frequency}} that is proportional to the square root of {\it{energy}}. On the other hand, the phase diagram does not reveal a closed structure since there is a singularity in the momentum even though energy remains finite. The generally covariant form is related to a generalization of the Snyder algebra in a specific gauge and yields the $κ$-Minkowski spacetime after a redefinition of the variables. Symmetry considerations are also briefly discussed in the Hamiltonian formulation. Regarding continuous symmetry, the angular momentum acts properly as the generator of rotation. Interestingly, both the discrete symmetries, parity and time reversal, remain intact in the $κ$-Minkowski spacetime.

hep-th↗
arXiv2005

Noncommutativity in Maxwell-Chern-Simons-Matter Theory Simulates Pauli Magnetic Coupling

We study interactions between like charges in the noncommutative Maxwell-Chern-Simons electrodynamics {\it{minimally}} coupled to spinors or scalars. We demonstrate that the non-relativistic potential profiles, for only spatial noncommutativity, are nearly identical to the ones generated by a {\it{non-minimal}} Pauli magnetic coupling, originally introduced by Stern \cite{js}. Although the Pauli term has crucial roles in the context of physically relevant objects such as anyons and like-charge bound states (or "Cooper pairs"), its inception \cite{js} (see also \cite{others}) was ad-hoc and phenomenological in nature. On the other hand we recover similar results by extending the minimal model to the noncommutative plane, which has developed in to an important generalization to ordinary spacetime in recent years. No additional input is needed besides the noncommutativity parameter. We prove a novel result that for complex scalar matter sector, the bound states (or "Cooper pairs" can be generated {\it{only}} if the Maxwell-Chern-Simons-scalar theory is embedded in noncommutative spacetime. This is all the more interesting since the Chern-Simons term does not directly contribute a noncommutative correction term in the action.

hep-th↗
arXiv2004

Extended Space Duality in the Noncommutative Plane

Non-Commutative (NC) effects in planar quantum mechanics are investigated. We have constructed a {\it{Master}} model for a noncommutative harmonic oscillator by embedding it in an extended space, following the Batalin-Tyutin \cite{bt} prescription. Different gauge choices lead to distinct NC structures, such as NC coordinates, NC momenta or noncommutativity of a more general kind. In the present framework, all of these can be studied in a unified and systematic manner. Thus the dual nature of theories having different forms of noncommutativity is also revealed.

hep-th↗
arXiv2004

Wavepackets and Duality in Noncommutative Planar Quantum Mechanics

Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative effects in a Gaussian wavepacket through the broadening of its width. We also rederive results on *-product of Gaussian wavepackets. In the second part, we construct a "Master" model for a noncommutative harmonic oscillator by embedding it in an extended space. Different gauge choices leading to different forms of noncommutativity, (such as between coordinates only, between momenta only or noncommutativity of a more general kind), can be studied in a unified and systematic manner. Thus the dual nature of these theories are also revealed.

hep-th↗
arXiv2004

Space-Time Symmetries in Noncommutative Gauge Theory: A Hamiltonian Analysis

We study space-time symmetries in Non-Commutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in \cite{sg}, has been considered. Subtle features of Lorentz invariance violation in NC field theory were pointed out in \cite{har}. Out of the two - Observer and Particle - distinct types of Lorentz transformations, symmetry under the former, (due to the translation invariance), is reflected in the conservation of energy and momentum in NC theory. The constant tensor $θ_{μν}$ (the noncommutativity parameter) destroys invariance under the latter. In this paper we have constructed the Hamiltonian and momentum operators which are the generators of time and space translations respectively. This is related to the Observer Lorentz invariance. We have also shown that the Schwinger condition and subsequently the Poincare algebra is not obeyed and that one can not derive a Lorentz covariant dynamical field equation. These features signal a loss of the Particle Lorentz symmetry. The basic observations in the present work will be relevant in the Hamiltonian study of a generic noncommutative field theory.

hep-th↗
arXiv2004

Noncommutative Chern-Simons Soliton

We have studied the noncommutative extension of the relativistic Chern-Simons-Higgs model, in the first non-trivial order in $θ$, with only spatial noncommutativity. Both Lagrangian and Hamiltonian formulations of the problem have been discussed, with the focus being on the canonical and symmetric forms of the energy-momentum tensor. In the Hamiltonian scheme, constraint analysis and the induced Dirac brackets have been provided. The spacetime translation generators and their actions on the fields are discussed in detail. The effects of noncommutativity on the soliton solutions have been analysed thoroughly and we have come up with some interesting observations. Considering the {\it{relative}} strength of the noncommutative effects, we have shown that there is a universal character in the noncommutative correction to the magnetic field - it depends {\it{only}} on $θ$. On the other hand, in the cases of all other observables of physical interest, such as the potential profile, soliton mass or the electric field, $θ$ as well as $τ$, (comprising solely of commutative Chern-Simons-Higgs model parameters), appear on similar footings. This phenomenon is a new finding which has come up in the present analysis. Lastly, we have pointed out a generic problem in the NC extension of the models, in the form of a mismatch between the BPS dynamical equation and the full variational equations of motion, to $O(θ)$. This mismatch indicates that the analysis is not complete as it brings in to fore the ambiguities in the definition of the energy-momentum tensor in a noncommutative theory.

hep-th↗
arXiv2004

Maxwell-Chern-Simons Theory is Free for Marginally Noncommutative Spacetimes

We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter $θ^{μν}$, with $θ^{0i}=0$. This shows that the former theory is free for marginally noncommutative spacetimes. A $θ$-generalized covariant mapping between the variables of the two models in question has been derived explicitly, that converts one model to the other, including the symplectic structure and action.

hep-th↗
arXiv2003

Soldering Formalism in Noncommutative Field Theory: A Brief Note

In this paper, I develop the Soldering formalism in a new domain - the noncommutative planar field theories. The Soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into account the interference effects. The above mentioned symmetry is hidden in the composite (or soldered) theory. In the present work it is shown that a pair of noncommutative Maxwell-Chern-Simons theories, having opposite signs in their respective topological terms, can be consistently soldered to yield the Proca model (Maxwell theory with a mass term) with corrections that are at least quadratic in the noncommutativity parameter. We further argue that this model can be thought of as the noncommutative generalization of the Proca theory of ordinary spacetime. It is well-known that abelian noncommutative gauge theory bears a close structural similarity with non-abelian gauge theory. This fact is manifested in a non-trivial way if the present work is compared with existing literature, where soldering of non-abelian models are discussed. Thus the present work further establishes the robustness of the soldering programme. The subtle role played by gauge invariance, (or the lack of it), in the above soldering process, is revealed in an interesting way.

hep-th↗
arXiv2003

Energy Crisis or a New Soliton in the Noncommutative CP(1) Model?

The Non-Commutative (NC) CP(1) model is studied from field theory perspective. Our formalism and definition of the NC CP(1) model differs crucially from the existing one \cite{nccp}. Due to the U(1) gauge invariance, the Seiberg-Witten map is used to convert the NC action to an action in terms of ordinary spacetime degrees of freedom and the subsequent theory is studied. The NC effects appear as (NC parameter) $θ$-dependent interaction terms. The expressions for static energy, obtained from both the symmetric and canonical forms of the energy momentum tensor, are {\it {identical}}, when only spatial noncommutativity is present. Bogomolny analysis reveals a lower bound in the energy in an unambiguous way, suggesting the presence of a new soliton. However, the BPS equations saturating the bound are not compatible to the full variational equation of motion. This indicates that the definitions of the energy momentum tensor for this particular NC theory, (the NC theory is otherwise consistent and well defined), are inadequate, thus leading to the "energy crisis". A collective coordinate analysis corroborates the above observations. It also shows that the above mentioned mismatch between the BPS equations and the variational equation of motion is small.

hep-th↗
arXiv2003

The Seiberg-Witten Map in Noncommutative Field Theory: An Alternative Interpretation

In this article, an alternative interpretation of the Seiberg-Witten map in non-commutative field theory is provided. We show that the Seiberg-Witten map can be induced in a geometric way, by a field dependent co-ordinate transformation that connects noncommutative and ordinary space-times. Furthermore, in continuation of our earlier works, it has been demonstrated here that the above (field dependent co-ordinate) transformations are present in a gauge fixed version of the relativistic spinning particle model, embedded in the Batalin-Tyutin extended space. We emphasize that the space-time non-commutativity emerges naturally from the particle {\it {spin}} degrees of freedom. Contrary to similarly motivated works, the non-commutativity is not imposed here in an {\it{ad-hoc}} manner.

hep-th↗
arXiv2003

A New Interpretation of the Seiberg Witten Map

In an alternative interpretation, the Seiberg-Witten map is shown to be induced by a field dependent co-ordinate transformation connecting noncommutative and ordinary space-times. Furthermore, following our previous ideas, it has been demonstrated here that the above (field dependent co-ordinate) transformation can occur naturally in the Batalin-Tyutin extended space version of the relativistic spinning particle model, (in a particular gauge). There is no need to postulate the space-time non-commutativity in an {\it ad hoc} way: It emerges from the spin degrees of freedom.

hep-th↗
arXiv2003

Bosonization in the Noncommutative Plane

In this Note, we study bosonization of the noncommutative massive Thirring model in 2+1- dimensions. We show that, contrary to the duality between massive Thirring model and Maxwell-Chern-Simons model in ordinary spacetime, in the low energy (or large fermion mass) limit, their noncommutative versions are not equivalent, in the same approximation.

hep-th↗
arXiv2003

Gauge Invariance and Duality in the Noncommutative Plane

We show that the duality between the self-dual and Maxwell-Chern-Simons theories in 2+1-dimensions survives when the space-time becomes noncommutative. Existence of the Seiberg-Witten map is crucial in the present analysis. It should be noted that the above models, being manifestly gauge variant and invariant respectively, transform differently under the Seiberg-Witten map. We also discuss this duality in the Stuckelberg formalism where the self-dual model is elevated to a gauge theory. The "`master"' lagrangian approach has been followed throughout.

hep-th↗
arXiv2002

"Gauging" the Fluid

A consistent framework has been put forward to quantize the isentropic, compressible and inviscid fluid model in the Hamiltonian framework, using the Clebsch parameterization. The naive quantization is hampered by the non-canonical (in particular field dependent) Poisson Bracket algebra. To overcome this problem, the Batalin-Tyutin \cite{12} quantization formalism is adopted in which the original system is converted to a local gauge theory and is embedded in a {\it canonical} extended phase space. In a different reduced phase space scheme \cite{vy} also the original model is converted to a gauge theory and subsequently the two distinct gauge invariant formulations of the fluid model are related explicitly. This strengthens the equivalence between the relativistic membrane (where a gauge invariance is manifest) and the fluid (where the gauge symmetry is hidden). Relativistic generalizations of the extended model is also touched upon.

hep-th↗