Browsing by Author "Bhabani Prasad Mandal"

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A black potential for spin less particles
(Elsevier B.V., 2015) Ananya Ghatak; Mohammad Hasan; Bhabani Prasad Mandal
We consider the most general non-Hermitian Hulthen potential to study the scattering of spin-less relativistic particles. The conditions for CC, SS and CPA are obtained analytically for this potential. We show that almost total absorption occurs for entire range of incidence energy for certain parameter ranges of the potential and hence term this as 'black potential'. Time reversed of the same potential shows perfect emission for the entire range of particle energy. We also present the classical analog of this potential in terms of waveguide cross section. © 2015 Elsevier B.V. All rights reserved.
A class of exactly solvable rationally extended Calogero–Wolfes type 3-body problems
(Academic Press Inc., 2017) Nisha Kumari; Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
In this work, we start from the well known Calogero–Wolfes type 3-body problems on a line and construct the corresponding exactly solvable rationally extended 3-body potentials. In particular, we obtain the corresponding energy eigenvalues and eigenfunctions which are in terms of the product of Xm Laguerre and Xp Jacobi exceptional orthogonal polynomials where both m,p=1,2,3,. © 2017 Elsevier Inc.
A class of exactly solvable rationally extended non-central potentials in two and three dimensions
(American Institute of Physics Inc., 2018) Nisha Kumari; Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
We start from a seven parameter (six continuous and one discrete) family of non-central exactly solvable potentials in three dimensions and construct a wide class of ten parameters (six continuous and four discrete) family of rationally extended exactly solvable non-central real as well as PT symmetric complex potentials. The energy eigenvalues and the eigenfunctions of these extended non-central potentials are obtained explicitly and it is shown that the wave eigenfunctions of these potentials are either associated with the exceptional orthogonal polynomials or some type of new polynomials which can be further re-expressed in terms of the corresponding classical orthogonal polynomials. Similarly, we also construct a wide class of rationally extended exactly solvable non-central real as well as complex PT-invariant potentials in two dimensions. © 2018 Author(s).
A class of exactly solvable real and complex PT symmetric reflectionless potentials
(American Institute of Physics Inc., 2024) Suman Banerjee; Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
We consider the question of the number of exactly solvable complex but PT-invariant reflectionless potentials with N bound states. By carefully considering the Xm rationally extended reflectionless potentials, we argue that the total number of exactly solvable complex PT-invariant reflectionless potentials are 2[(2N − 1)m + N]. © 2024 Author(s).
A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46–54]
(Academic Press Inc., 2017) Arturo Ramos; Bijan Bagchi; Avinash Khare; Nisha Kumari; Bhabani Prasad Mandal; Rajesh Kumar Yadav
It is proved the equivalence of the compatibility condition of Ramos (2011, 2012) with a condition found in Yadav et al. (2015). The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xℓ Jacobi and Laguerre cases are given. © 2017 Elsevier Inc.
A Superspace Description of Chern-Simons Theory in Batalin-Vilkovisky Formulation
(Springer New York LLC, 2015) Sudhaker Upadhyay; Manoj Kumar Dwivedi; Bhabani Prasad Mandal
We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for the Chern-Simons (CS) theories in (2 + 1) spacetime dimensions. Further we develop the superspace description of BV formulation for such theories. Interestingly, the extended BRST invariant CS theories can be described in superspace in covariant manner with the help of one more (Grassmann) coordinate. However, a superspace with two Grassmann coordinates are required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant actions for these theories. © 2014, Springer Science+Business Media New York.
A unifying framework for BRST and BRST-related symmetries
(Institute of Physics, 2023) Bhabani Prasad Mandal; Sumit Kumar Rai; Ronaldo Thibes
We propose a general framework to study BRST-related transformations. We investigate different forms of BRST and BRST-related symmetries, realized within a prototypical first-class system, including ordinary BRST, anti-BRST, dual-BRST, anti-dual-BRST and additional sets of new BRST-related symmetries. We identify a precise discrete group of symmetries of the ghost sector, responsible for connecting the various forms of BRST-related transformations. Their distinct roles in different Hamiltonian and Lagrangian approaches are clarified. As a unifying framework, we use a gauge invariant prototypical first-class system encompassing an extensive class of physical models. Copyright © 2023 The author(s)
BFV quantization and BRST symmetries of the gauge invariant fourth-order Pais-Uhlenbeck oscillator
(Elsevier B.V., 2022) Bhabani Prasad Mandal; Vipul Kumar Pandey; Ronaldo Thibes
We perform the BFV-BRST quantization of the fourth-order Pais-Uhlenbeck oscillator (PUO) for the first time. We show that although the PUO is not naturally constrained in the sense of Dirac-Bergmann, it is possible to profit from the introduction of suitable constraints in phase space in order to obtain a proper BRST invariant quantum system. Starting from its second-class constrained system description, we use the BFFT formalism to obtain first-class constraints as gauge symmetry generators. After the Abelianization of the constraints, we obtain the conserved BRST charge, the corresponding BRST transformations and proceed further to the BFV functional quantization of the model. We further construct appropriate finite field dependent BRST transformation to establish the interconnections between different BRST invariant effective theories of PUO in different gauges. Our approach sheds light on the open problem of the quantization of general higher derivative quantum field theories. © 2022 The Author(s)
BRST Qantization on Torus Knot
(Springer Science and Business Media, LLC, 2018) Vipul Kumar Pandey; Bhabani Prasad Mandal
Knot Theory is a branch of mathematics which has found many application in high energy and condensed matter physics. We develop BRST/anti-BRST formulation for particle on a torus knot. © 2018, Springer International Publishing AG, part of Springer Nature.
BRST symmetry as a mechanism for confinement in the inter gauge framework
(Elsevier B.V., 2022) Haresh Raval; Bhabani Prasad Mandal
The finite field dependent BRST (FFBRST) technique generally interrelates two different gauge fixed theories. Here we propose a new and unique FFBRST transformation that transforms the effective theory in Lorenz gauge, which represents perturbative or deconfined phase of QCD to massive gauge theory. The exercise serves two purposes. First is of course that it is a distinct connection where one of the theories is not gauge fixed and BRST invariant therefore, it is expected to give newer insights into FFBRST technique itself. Second is that a particular case of this transformation holds a novel physical significance of acting as general mechanism for confinement across two different gauge theories. Thus, the present task identifies a profound non-perturbative implication of the BRST symmetry in a general setting. © 2022
BRST symmetry for a torus knot
(Institute of Physics Publishing, 2017) Vipul Kumar Pandey; Bhabani Prasad Mandal
We develop BRST symmetry for the first time for a particle on the surface of a torus knot by analyzing the constraints of the system. The theory contains 2nd-class constraints and has been extended by introducing the Wess-Zumino term to convert it into a theory with first-class constraints. BFV analysis of the extended theory is performed to construct BRST/anti-BRST symmetries for the particle on a torus knot. The nilpotent BRST/anti-BRST charges which generate such symmetries are constructed explicitly. The states annihilated by these nilpotent charges consist of the physical Hilbert space. We indicate how various effective theories on the surface of the torus knot are related through the generalized version of the BRST transformation with finite-field-dependent parameters. © CopyrightEPLA, 2017.
BV formulation of higher form gauge theories in a superspace
(Springer New York LLC, 2012) Sudhaker Upadhyay; Bhabani Prasad Mandal
We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for 2- and 3-form gauge theories. Further we develop the superspace formulation for the BV actions for these theories. We show that the extended BRST invariant BV action for these theories can be written manifestly covariant manner in a superspace with one Grassmann coordinate. On the other hand a superspace with two Grassmann coordinates is required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant BV actions for higher form gauge theories. © 2012 Springer-Verlag / Società Italiana di Fisica.
Comments on interactions in the SUSY models
(Springer New York LLC, 2016) Sudhaker Upadhyay; Alexander Reshetnyak; Bhabani Prasad Mandal
We consider special supersymmetry (SUSY) transformations with m generators s← α, for some class of models and study the physical consequences when making the Grassmann-odd transformations to form an Abelian supergroup with finite parameters and a set of group-like elements with finite parameters being functionals of the field variables. The SUSY-invariant path integral measure within conventional quantization scheme leads to the appearance of the Jacobian under a change of variables generated by such SUSY transformations, which is explicitly calculated. The Jacobian implies, first of all, the appearance of trivial interactions in the transformed action, and, second, the presence of a modified Ward identity which reduces to the standard Ward identities in the case of constant parameters. We examine the case of the N= 1 and N= 2 supersymmetric harmonic oscillators to illustrate the general concept by a simple free model with (1, 1) physical degrees of freedom. It is shown that the interaction terms Utr have a corresponding SUSY-exact form: Utr= (V(1)s← ; V(2)s¯ ← s←) generated naturally under such generalized formulation. We argue that the case of a non-trivial interaction cannot be obtained in such a way. © 2016, The Author(s).
Comparison of different approaches of finding the positive definite metric in pseudo-Hermitian theories
(2013) Ananya Ghatak; Bhabani Prasad Mandal
To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models. © 2013 Chinese Physical Society and IOP Publishing Ltd.
Complex Classical Mechanics of a QES Potential
(Institute of Physics Publishing, 2015) Bhabani Prasad Mandal; Sushant S. Mahajan
We study a combined parity (P) and time reversal (T) invariant non-Hermitian quasi-exactly solvable (QES) potential, which exhibits PT phase transition, in the complex plane classically to demonstrate different quantum effects. The particle with real energy makes closed orbits around one of the periodic wells of the complex potential depending on the initial condition. However interestingly the particle escapes to an open orbits even with real energy if it is placed beyond a certain distance from the center of the well. On the other hand when the particle energy is complex the trajectory is open and the particle tunnels back and forth between two wells which are separated by a classically forbidden path. The tunneling time is calculated for different pair of wells and is shown to vary inversely with the imaginary component of energy. Our study reveals that spontaneous PT symmetry breaking does not affect the qualitative features of the particle trajectories in the analogous complex classical model. ï¿½ 2015 Chinese Physical Society and IOP Publishing Ltd.
Conformal to harmonic gauge for bosonic strings
(Institute of Physics Publishing, 2019) Vipul Kumar Pandey; Bhabani Prasad Mandal
We consider the Polyakov theory of bosonic strings in conformal gauge which are used to study the conformal anomaly. However, it exhibits ghost number anomaly. We show how this anomaly can be avoided by connecting this theory to that of in background covariant harmonic gauge which is known to be free from conformal and ghost number current anomaly, by using suitably constructed finite-field-dependent BRST transformation. © CopyrightEPLA, 2019.
Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system
(2014) Mohammad Hasan; Ananya Ghatak; Bhabani Prasad Mandal
We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system. © 2014 Elsevier Inc.
Deconfinement to confinement as PT phase transition
(Elsevier B.V., 2019) Haresh Raval; Bhabani Prasad Mandal
We consider SU(N) QCD in a new quadratic gauge which highlights certain characteristic of the theory in the non-perturbative sector. By considering natural hermiticity property of the ghost fields we cast this model as non-Hermitian but symmetric under combined Parity (P) and Time reversal (T) transformations. We explicitly study the PT phase transition in this model. This is very first such study in the non-Hermitian gauge theory. The ghost fields condensate which give rise to spontaneous breaking of PT symmetry. This leads to realize the transition from deconfined phase to confined phase as a PT phase transition in this system. The hidden C-symmetry in this system is identified as inner automorphism in this theory. Explicit representation is constructed for the C-symmetry. © 2019 The Authors
Deconfinement to Confinement as PT Phase Transition
(Springer Science and Business Media Deutschland GmbH, 2021) Haresh Raval; Bhabani Prasad Mandal
We consider SU(N) QCD in a new quadratic gauge which highlights a certain characteristic of the theory in the non-perturbative sector. By considering the natural hermiticity property of the ghost fields, we cast this model as non-Hermitian but symmetric under combined Parity (P) and Time reversal (T) transformations. We explicitly study the PT phase transition in this model. This is the very first such study in the non-Hermitian gauge theory. The ghost fields condensate which give rise to spontaneous breaking of PT symmetry. This leads to realize the transition from deconfined phase to confined phase as a PT phase transition in this system. The hidden C-symmetry in this system is identified as inner automorphism in this theory. Explicit representation is constructed for the C-symmetry. © 2021, Springer Nature Singapore Pte Ltd.
Delayed pulsar kicks from the emission of sterile neutrinos
(2008) Alexander Kusenko; Bhabani Prasad Mandal; Alok Mukherjee
The observed velocities of pulsars suggest the possibility that sterile neutrinos with mass of several keV are emitted from a cooling neutron star. The same sterile neutrinos could constitute all or part of cosmological dark matter. The neutrino-driven kicks can exhibit delays depending on the mass and the mixing angle, which can be compared with the pulsar data. We discuss the allowed ranges of sterile neutrino parameters, consistent with the latest cosmological and x-ray bounds, which can explain the pulsar kicks for different delay times. © 2008 The American Physical Society.