arXiv subjects

Rabin Banerjee

Publications and source records attributed to Rabin Banerjee.

At least 19 recordsLinked to original sources

arXiv2025

Null reduction and dynamical realization of Carrollian conformal symmetries

We start from a Lorentzian action in a deformed light-cone background and applying the method of null reduction leads to a Carrollian action in one lower spacetime dimensions. We also identify the correct light-cone definitions of the symmetry generators and their dynamical forms in terms of the fields and take the $c\rightarrow0$ limit. It is observed that these generators produce the known kinematic Carrollian conformal algebraic commutation relations.

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arXiv2025

Gauge interactions and the Galilean limit

The gauge invariant minimal couplings for a class of relativistic free matter fields with global symmetry (related to usual charge conservation) have been obtained by incorporating an iterative Noether mechanism. Non-relativistic reduction of both matter and gauge sectors of the obtained interacting theory is then performed simultaneously which in turn yield a set of new effective actions which are invariant under the Galilean relativistic framework. To be precise, we show that one can obtain the Schr\"odinger field theory coupled to Galilean electromagnetism from the scalar quantum electrodynamics theory. Higher derivative corrections have also been included for which the non-relativistic reductions have been consistently carried out once again. On the other hand, the action for quantum electrodynamics leads to the Galilean Pauli-Schr\"odinger theory where the gauge field is non-relativistic or Galilean. Further, some novel relations are found (in both the electric and magnetic limits) between various components appearing in the Galilean avatar of electrodynamics.

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arXiv2024

SVD Entanglement Entropy of Chiral Dirac Oscillators

We discuss the SVD entanglement entropy, which has recently come up as a successor to the pseudo entropy. This paper is a first of-its-kind application of SVD entanglement entropy to a system of chiral Dirac oscillators which prove to be a natural system to study the SVD formalism because the two chiral oscillator ground states can be taken as the pre-selected and post-selected states. We argue how this alternative for entanglement entropy is better and more intuitive than the von Neumann one to study quantum phase transition. It is shown that SVD entropy diverges at the critical point, matching von Neumann entropy in the left-handed regime but differing in the right-handed regime. We also provide as an illustrative example, a new generalized proof of the SVD entanglement entropy being log2 for a pair of Bell states that differ from each other by relative phases

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arXiv2024

Sengupta Transformations and Carrollian Relativistic Theory

A detailed and systematic formulation of Carrollian relativity is provided. Based on the transformations, first provided by Sengupta [19], we construct a mapping between Lorentz relativistic and Carrollian relativistic vectors. Using this map the Carroll theory is built from the standard Maxwell action. We show that we get self-consistent equations of motion from the action, both in electric and magnetic limits. We introduce Carroll electric and magnetic fields. A new set of maps is derived that connects Carroll electric and magnetic fields with the usual Maxwell ones and yields Carroll equations in terms of fields. Consistency of results with the potential formulation is shown. Carroll version of symmetries like duality, gauge, shift, Noether and boost are treated in details and their implications elaborated. Especially, boost symmetry provides a link to the various maps used in this paper.

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arXiv2023

Formulation of Galilean relativistic Born-Infeld theory

In this paper, we formulate, for the first time, in a systematic manner, Galilean relativistic Born-Infeld action in detail. Exploiting maps connecting Lorentz relativistic and Galilean relativistic vectors, we construct the two limits (electric and magnetic) of Galilean relativistic Born-Infeld action from usual relativistic Born-Infeld theory. An action formalism is thereby derived. From this action, equations of motion are obtained either in the potential or field formulation. Galilean version of duality transformations involving the electric and magnetic fields are defined. They map the electric limit relations to the magnetic ones and vice-versa, exactly as happens for Galilean relativistic Maxwell theory. We also explicitly show the Galilean boost and gauge invariances of the theory in both limits.

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arXiv2023

Action principle of Galilean relativistic Proca theory

In this paper, we discuss Galilean relativistic Proca theory in detail. We first provide a set of mapping relations, derived systematically, that connect the covariant and contravariant vectors in the Lorentz relativistic and Galilean relativistic formulations. Exploiting this map, we construct the two limits of Galilean relativistic Proca theory from usual Proca theory in the potential formalism for both contravariant and covariant vectors which are now distinct entities. An action formalism is thereby derived from which the field equations are obtained and their internal consistency is shown. Next we construct Noether currents and show their on-shell conservation. We introduce analogues of Maxwell's electric and magnetic fields and recast the entire analysis in terms of these fields. Explicit invariance under Galilean transformations is shown for both electric/magnetic limits. We then move to discuss Stuckelberg embedded Proca model in the Galilean framework.

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arXiv2022

New formulation of Galilean relativistic Maxwell theory

In this paper, we discuss Galilean relativistic Maxwell theory in detail. We first provide a set of mapping relations, derived systematically, that connect the covariant and contravariant vectors in the Lorentz relativistic and Galilean relativistic formulations. Exploiting this map, we construct the two limits of Galilean relativistic Maxwell theory from usual Maxwell's theory in the potential formalism for both contravariant and covariant vectors which are now distinct entities. Field equations are derived and their internal consistency is shown. The entire analysis is then performed in terms of electric and magnetic fields for both covariant and contravariant components. Duality transformations and their connection with boost symmetry are discussed which reveal a rich structure. The notion of twisted duality is introduced. Next we consider gauge symmetry, construct Noether currents and show their on-shell conservation. We also discuss shift symmetry under which the Lagrangian is invariant, where the corresponding currents are now on-shell conserved. At the end we analyse the theory by including sources for both contravariant and covariant sectors. We show that sources are now off-shell conserved

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arXiv2022

Shift symmetries and duality web in gauge theories

Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the basis for revealing a dual picture when the full interacting theory is considered by coupling to gauge fields. The coupling is achieved in terms of vector fields by adhering to a modified minimal prescription which is also supported by an iterative Noether scheme. Further, this scheme shows that couplings can also be introduced using higher rank tensor gauge fields that have appeared in recent discussions on fractons. We reveal a connection among these descriptions (using vector or tensor fields) through certain duality maps that relate the various fields (gauge, electric and magnetic) in the two cases. A correspondence is established among the Gauss' law, Faraday's law and Ampere's law. Explicit calculations are provided for linear and quadratic shift symmetric lagrangians.

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arXiv2022

Cosmic Acceleration and the notion of Alternative Vacuum in Nash Theory

We argue that Nash theory, a quadratic theory of Gravity, can describe a late-time cosmic acceleration without any exotic matter or cosmological constant. The observational viability of an exact cosmological solution of Nash theory is adjudged using a Markov chain Monte Carlo simulation and JLA+OHD+BAO data sets. Departures from standard {\Lambda}CDM cosmology are noted and analyzed. We prove that the Nash vacuum dynamics is equivalent to the dynamics of an Einstein vacuum plus a self-interacting Higgs scalar field, only if a mild evolution of the Higgs Vacuum Expectation Value is allowed. This leads to variations in the mass scales of fundamental particles and the fine structure constant. The variations are found to fit nicely with the analysis of molecular absorption spectra from a series of Quasars.

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arXiv2022

Noether type formulation for space dependent polynomial symmetries

We develop a systematic algorithm, based on Noether's theorem, for defining the various currents in theories invariant under space dependent polynomial symmetries. A master equation is given that yields all the conservation laws corresponding to these currents. Explicit demonstration has been provided for dipole and quadrupole conservation symmetries.

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arXiv2021

Dual Description of Gauge Theories from an Iterative Noether Approach

An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic theories. No reference to any gauge principle, fractonic or otherwise, is required. A dual description is found where the theory is defined either in terms of the usual vector gauge field or, alternatively, in terms of higher derivatives of a symmetric tensor field. A connection between these two descriptions is obtained by providing an explicit map between the vector and tensor fields. This method yields a novel `minimal' prescription for the tensor fields which is identified with the usual minimal prescription for the vector fields by using the mapping. It also spells out the structure of the pure gauge field action in both formulations. Extension of the abelian $U(1)$ invariance to the nonabelian $SU(N)$ invariance is done for the standard formulation.

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arXiv2021

Covariant Formulation of the Newton-Hooke Particle and its Canonical Analysis

A covariant formulation for the Newton-Hooke particle is presented by following an algorithm developed by us \cite{BMM1, BMM2, BMM3}. It naturally leads to a coupling with the Newton-Cartan geometry. From this result we provide an understanding of gravitation in a Newtonian geometric background. Using Dirac's constrained analysis a canonical formulation for the Newton-Hooke covariant action is done in both gauge independent and gauge fixed approaches. While the former helps in identifying the various symmetries of the model, the latter is able to define the physical variables. From this analysis a path to canonical quantisation is traced and the Schroedinger equation is derived which is shown to satisfy various consistency checks. Some consequences of this equation are briefly mentioned.

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arXiv2021

Hamiltonian Formulation of Higher Rank Symmetric Gauge Theories

Recent discussions of higher rank symmetric (fractonic) gauge theories have revealed the important role of Gauss constraints. This has prompted the present study where a detailed hamiltonian analysis of such theories is presented. Besides a general treatment, the traceless scalar charge theory is considered in details. A new form for the action is given which, in 2+1 dimensions, yields area preserving diffeomorphisms. Investigation of global symmetries reveals that this diffeomorphism invariance induces a noncommuting charge algebra that gets exactly mapped to the algebra of coordinates in the lowest Landau level problem. Connections of this charge algebra to noncommutative fluid dynamics and magnetohydrodynamics are shown.

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arXiv2020

Demystification of Non-relativistic Theories in Curved Background

We discuss a new formalism for constructing a non-relativistic (NR) theory in curved background. Named as galilean gauge theory, it is based on gauging the global galilean symmetry. It provides a systematic algorithm for obtaining the covariant curved space time generalisation of any NR theory defined in flat space time. The resulting background is just the Newton- Cartan manifold. The example of NR free particle is explicitly demonstrated.

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arXiv2020

A new approach for nonrelativistic bosonic string in flat space time

A new approach to the study of nonrelativistic bosonic string in flat space time is introduced, basing on a holistic hamiltonian analysis of the minimal action for the string. This leads to a structurally new form of the action which is, however, equivalent to the known results since, under appropriate limits, it interpolates between the minimal action (Nambu Goto type) where the string metric is taken to be that induced by the embedding and the Polyakov type of action where the world sheet metric components are independent fields. The equivalence among different actions is established by a detailed study of symmetries using constraint analysis. Various vexing issues in the existing literature are clarified. The interpolating action mooted here is shown to reveal the geometry of the string and may be useful in analyzing nonrelativistic string coupled with curved background.

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arXiv2020

Canonical Formulation of a New Action for a Non-relativistic Particle Coupled to Gravity

A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy the geodesic equation in the Newton-Cartan background, thereby clearing certain confusions. The Hamiltonian analysis is done in the gauge independent as well as gauge fixed approaches, following Dirac's analysis of constraints. The physical (canonical) variables are identified and the path to canonical quantisation is outlined by explicitly deriving the Schroedinger equation.

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arXiv2020

Fluctuation-Dissipation relation from anomalous stress tensor and Hawking effect

We show a direct connection between Kubo's fluctuation-dissipation relation and Hawking effect that is valid in any dimensions for any stationary or static black hole. The relevant correlators corresponding to the fluctuating part of the force, computed from the known expressions for the anomalous stress tensor related to gravitational anomalies, are shown to satisfy the Kubo relation, from which the temperature of a black hole as seen by an observer at an arbitrary distance is abstracted. This reproduces the Tolman temperature and hence the Hawking temperature as that measured by an observer at infinity.

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arXiv2020

Non-relativistic Reduction of Spinors, New Currents and their Algebra

A specific mapping is introduced to reduce the Dirac action to the non-relativistic (Pauli - Schrödinger) action for spinors. Using this mapping, the structures of the vector and axial vector currents in the non-relativistic theory are obtained. The implications of the relativistic Ward identities in the non-relativistic limit are discussed. A new non-abelian type of current in the Pauli - Schrödinger theory is obtained. As we show, this is essential for the closure of the algebra among the usual currents. The role of parity in the non-relativistic theory is also discussed.

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