arXiv subjects

Rabin Banerjee

Publications and source records attributed to Rabin Banerjee.

At least 55 records · Page 3Linked to original sources

arXiv2016

New approach to nonrelativistic diffeomorphism invariance and its applications

A comprehensive account of a new structured algorithm for obtaining nonrelativistic diffeomorphism invariances in both space and spacetime by gauging the Galilean symmetry in a generic nonrelativistic field theoretical model is provided. Various applications like the obtention of nonrelativistic diffeomorphism invariance, the introduction of Chern-Simons term and its role in fractional quantum Hall effect, induction of diffeomorphism in irrotational fluid model, abstraction of Newton-Cartan geometry and the emergence of Horava-Lifshitz gravity are discussed in details.

gr-qc↗

arXiv2015

Dynamical construction of Horava-Lifshitz geometry

We derive the projectable version of Horava - Lifshitz gravity from the localisation of the Galilean symmetry. Specifically we provide a dynamical construction of the metric, from first principles, that reproduces the transformations of the physical variables - lapse, shift and spatial component of the metric. Also, the measure defining the action is reproduced. The geometrical basis of the Horava-Lifshitz gravity is thereby revealed which also elucidates its difference from the Newton-Cartan geometry - the spacetime of Newtonian gravity. The connection of Newton's gravity with Horava-Lifshitz gravity is elucidated.

hep-th↗

arXiv2015

Non relativistic diffeomorphism and the geometry of the fractional quantum Hall effect

We show that our recently proposed method\cite{BMM1,BMM2,BMM3,BM4} of constructing nonrelativistic diffeomorphism invariant field theories by gauging the Galilean symmetry provides a natural connection with the geometry of the fractional quantum Hall effect (FQHE). Specifically, the covariant derivative that appears on gauging, exactly reproduces the form that yields the Hall viscosity and Wen-Zee shift \cite{CYF}.

hep-th↗

arXiv2015

Elementary modes of coupled oscillators with balanced loss and gain

We obtain the elementary modes of a system of parity-time reversal ( PT ) - symmetric coupled oscillators with balanced loss and gain . These modes are used to give a physical picture of the phase transition recently reported in experiments with whispering - gallery microresonators.

hep-th↗

arXiv2015

Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters

The exact expression for the entropy current of a fluid in presence of two dimensional gravitational anomalies is given. To make it compatible with the second law of thermodynamics; i.e. positivity of the entropy production rate of a system (which is considered to be fundamental), we find a bound on the sum of the two response parameters ($\bar{C}_1$ and $\bar{C}_2$), in terms of the trace and diffeomorphism anomaly coefficients ($c_w$ and $c_g$). The precise expression, we obtain here, is $\bar{C}_1 + \bar{C}_2\leq 4π^2c_w + 8π^2 c_g$. Interestingly, when the bound is saturated corresponding to a reversible process, the result reproduces earlier findings obtained by either studying field theory on the cone or using the {\it Israel-Hartle-Hawking} boundary condition. Finally, possible physical implications and connections with the existing approaches are addressed.

hep-th↗

arXiv2015

Hamiltonian analysis of interacting fluids

Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical(Noether) stress tensor and the symmetric one obtained by metric variation are discussed. Finally, a non-relativistic reduction of the system in light-cone coordinates has been carried out which reproduces results found earlier in the literature.

hep-th↗

arXiv2015

$PT$ symmetry and a dynamical realization of the SU(1,1) algebra

We show that the elementary modes of the planar harmonic oscillator can be quantised in the framework of quantum mechanics based on pseudo-hermitian hamiltonians. These quantised modes are demonstrated to act as dynamical structures behind a new Jordan - Schwinger realization of the SU(1,1) algebra. This analysis complements the conventional Jordan - Schwinger construction of the SU(2) algebra based on hermitian hamiltonians of a doublet of oscillators.

quant-ph↗

arXiv2015

General algorithm for non-relativistic diffeomorphism invariance

An algorithmic approach towards the formulation of non-relativistic diffeomorphism invariance has been developed which involves both matter and gauge fields. A step by step procedure has been provided which can accommodate all types of (abelian) gauge interaction. The algorithm is applied to the problem of a two dimensional electron moving under an external field and also under the Chern-Simons dynamics.

gr-qc↗

arXiv2014

Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry

Newtonian gravity was formulated as a geometrodynamic theory as far back in 1930s by Elie Cartan in what is named aptly as Newton Cartan space time. Though there are several approaches of realizing the algebraic structure of the Newton Cartan geometry from a contraction of the relativistic results, a dynamical (field theoretic) realization of it is lacking. In this paper we present such a realization from the localisation of the Galilean Symmetry of nonrelativistic matter field theories.

hep-th↗

arXiv2014

A new formulation of non-relativistic diffeomorphism invariance

We provide a new formulation of nonrelativistic diffeomorphism invariance. It is generated by localising the usual global Galilean Symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the theory of fractional quantum Hall effect has been discussed. Our construction is shown to open up a general approach of model building in theoretical condensed matter physics. Also, this formulation has the capacity of obtaining Newton - Cartan geometry from the gauge procedure.

gr-qc↗

arXiv2014

Generalized supersymmetry and sigma models

In this paper, we discuss the generalizations of exact supersymmetries present in the supersymmetrized sigma models. These generalizations are made by making the supersymmetric transformation parameter field-dependent. Remarkably, the supersymmetric effective actions emerge naturally through the Jacobian associated with the generalized supersymmetry transformations. We explicitly demonstrate these for two different supersymmetric sigma models, namely, one dimensional sigma model and topological sigma model for hyperinstantons on quaternionic manifold.

hep-th↗

arXiv2014

Constitutive relations and response parameters in two dimensional hydrodynamics with gauge and gravitational anomalies

We obtain the constitutive relations for the stress tensor and gauge current in $(1+1)$ dimensional hydrodynamics in the presence of both gauge and gravitational (conformal as well as diffeomorphism) anomalies. The relations between response parameters and anomaly coefficients are also found. The role of the Israel-Hartle-Hawking vacuum is emphasized. Finally, in the absence of gauge fields, earlier results obtained by a hydrodynamic expansion are reproduced.

hep-th↗

arXiv2014

Two dimensional hydrodynamics with gauge and gravitational anomalies

We present a new approach to discuss two dimensional chiral and non-chiral hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. For the chiral theory, the constitutive relations may be put in the ideal (chiral) fluid form whereas the constitutive relations corresponding to non-chiral case do not take the ideal fluid form. The constitutive relations in the presence of both gravity and gauge sectors are new. These expressions, in the absence of the gauge sector, reproduce the results obtained in the gradient expansion approach.

hep-th↗

arXiv2014

Exact results in two dimensional chiral hydrodynamics with gravitational anomalies

An exact formulation of two dimensional chiral hydrodynamics with diffeomorphism and conformal anomalies is provided. The constitutive relation involving the stress tensor is computed. It reveals a one parameter class of solutions which is a new result. For a particular value of this parameter, the results found in the gradient expansion scheme are reproduced. Moreover, the constitutive relation is analogous to the corresponding relation for an ideal fluid, appropriately modified to include the chirality property, which has also been derived here.

gr-qc↗

arXiv2014

New Hamiltonian analysis of Regge Teitelboim minisuperspace cosmology

A new Hamiltonian formulation of the minisuperspace cosmology following from the geodetic brane gravity model introduced by Regge and Teitelboim is presented. The model is considered in the framework of higher derivative theories which facilitates Hamiltonian formulation. The analysis is done using the equivalent first order approach. The constraint algebra is shown to realize a truncated Virasoro algebra. The gauge generator containing the exact number of gauge parameters is constructed. Equivalence between the gauge and reparametrization symmetries has been demonstrated. Complete gauge fixed computations have been provided and formal quantization is indicated.

gr-qc↗

arXiv2013

New (Ghost-Free) Formulation of the Pais-Uhlenbeck Oscillator

We provide a new formulation of the Pais-Uhlenbeck oscillator which is a prototype of a higher derivative model. Different parametrisations that reveal the model as a combination of two simple harmonic oscillators are introduced. Conventional results are reproduced in one realisation. In another, all problems related to lack of unitarity or boundedness of energy are eliminated since the hamiltonian is expressed as a sum of the hamiltonians of two decoupled harmonic oscillators. Recourse to imaginary scaling transformation or PT-symmetry, as advocated in the literature, are totally avoided.

hep-th↗

arXiv2013

BRST symmetry and $W$-algebra in higher derivative models

In this paper we discuss the (anti-)BRST symmetries and $W$-algebra of higher derivative theories of relativistic particles satisfying general gauge conditions. Using this formalism, the connection between the (anti-)BRST symmetries and $W$-algebra for the rigid relativistic particle is established. Incidentally, the full $W$-algebra emerges only when the anti-BRST transformations are considered in tandem with the BRST ones. Further, the BRST symmetry is made finite and coordinate-dependent. We show that such finite coordinate-dependent BRST symmetry changes the BRST invariant gauge-fixing fermion within the functional integration. This is exploited to connect two different arbitrary gauge conditions.

hep-th↗

arXiv2013

Holographic s-wave condensate with non-linear electrodynamics: A nontrivial boundary value problem

In this paper, considering the probe limit, we analytically study the onset of holographic s-wave condensate in the planar Schwarzschild-AdS background. Inspired by various low energy features of string theory, in the present work we replace the conventional Maxwell action by a (non-linear) Born-Infeld (BI) action which essentially corresponds to the higher derivative corrections of the gauge fields. Based on a variational method, which is commonly known as the Sturm-Liouville (SL) eigenvalue problem and considering a non-trivial asymptotic solution for the scalar field, we compute the critical temperature for the s-wave condensation. The results thus obtained analytically agree well with the numerical findings\cite{hs19}. As a next step, we extend our perturbative technique to compute the order parameter for the condensation. Interestingly our analytic results are found to be of the same order as the numerical values obtained earlier.

hep-th↗