Browsing by Author "Sumit Kumar Rai"

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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)
Finite Nilpotent BRST Transformations in Hamiltonian Formulation
(2013) Sumit Kumar Rai; Bhabani Prasad Mandal
We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta. © 2013 Springer Science+Business Media New York.
Finite nilpotent symmetry in Batalin-Vilkovisky formalism
(2010) Bhabani Prasad Mandal; Sumit Kumar Rai; Sudhaker Upadhyay
We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories in the context of generalized BRST transformations with a finite field-dependent parameter. In the usual Faddeev-Popov (FP) formulation of gauge theories such finite fielddependent BRST (FFBRST) transformations do not leave the generating functionals invariant as the path integral measure changes in a non-trivial way for finite transformations. Here we show that FFBRST transformation, with the appropriate choice of a finite field-dependent parameter, is the symmetry of the generating functionals in the Batalin-Vilkovisky formalism. The finite parameter is chosen in such a way that the contribution from the Jacobian of the path integral measure is adjusted with gauge fixed fermions which do not change the generating functionals. Several examples for such finite parameters are constructed. Copyright © EPLA, 2010.
GUP corrections to the Dirac oscillator in the external magnetic field
(Institute of Physics Publishing, 2019) Vishakha Tyagi; Sumit Kumar Rai; Bhabani Prasad Mandal
We have studied the-dimensional Dirac oscillator (DO) in an external magnetic field in the framework of the generalized uncertainty principle (GUP). We have calculated the perturbative corrections for the first few energy levels. We show that the infinite degeneracy of lowest Landau level is partially lifted due to GUP correction and obtain a critical value of the magnetic field for which there is no GUP correction and the DO stops oscillating. © CopyrightEPLA, 2020.
New forms of brst symmetry in rigid rotor
(2010) Sumit Kumar Rai; Bhabani Prasad Mandal
We derive the different forms of BRST symmetry by using the BatalinFradkinVilkovisky formalism in a rigid rotor. The so-called "dual-BRST" symmetry is obtained from the usual BRST symmetry by making a canonical transformation in the ghost sector. On the other hand, a canonical transformation in the sector involving Lagrange multiplier and its corresponding momentum leads to a new form of BRST as well as dual-BRST symmetry. © 2010 World Scientific Publishing Company.
Noncommutative Dirac oscillator in an external magnetic field
(Elsevier B.V., 2012) Bhabani Prasad Mandal; Sumit Kumar Rai
We show that (2+1)-dimensional noncommutative Dirac oscillator in an external magnetic field is mapped onto the same but with reduced angular frequency in absence of magnetic field. We construct the relativistic Landau levels by solving corresponding Dirac equation in (2+1)-dimensional noncommutative phase space. All the Landau levels become independent of noncommutative parameter for a critical value of the magnetic field. Several other interesting features along with the relevance of such models in the study of atomic transitions in a radiation field have been discussed. © 2012 Elsevier B.V.
Off-shell nilpotent finite Becchi-Rouet-Stora-Tyutin (BRST)/anti-BRST transformations
(2011) Sudhaker Upadhyay; Sumit Kumar Rai; Bhabani Prasad Mandal
We develop the off-shell nilpotent finite field dependent Becchi-Rouet-Stora-Tyutin (BRST) transformations and show that for different choices of the finite field dependent parameter these transformations connect the generating functionals corresponding to different effective theories. We also construct both on-shell and off-shell finite field dependent anti-BRST transformations for Yang-Mills theories and show that these transformations play the similar role in connecting different generating functionals of different effective theories. Analogous to the finite field dependent BRST transformations, the nontrivial Jacobians of the path integral measure which arise due to the finite field dependent anti-BRST transformations are responsible for the new results. We consider several explicit examples in each case to demonstrate the results. © 2011 American Institute of Physics.
Relating the generating functionals in field/antifield formulation through finite field dependent BRST transformation
(2009) Sumit Kumar Rai; Bhabani Prasad Mandal
We study the field/antifield formulation of pure Yang Mills theory in the framework of the finite field dependent BRST transformation. We show that the generating functionals corresponding to different solutions of the quantum master equation are connected through the finite field dependent BRST transformations. We establish this result with the help of several explicit examples. © 2009 Springer-Verlag / Società Italiana di Fisica.
Various forms of BRST symmetry in Abelian 2-form gauge theory
(2011) Sumit Kumar Rai; Bhabani Prasad Mandal
We derive the various forms of BRST symmetry using BatalinFradkinVilkovisky approach in the case of Abelian 2-form gauge theory. We show that the so-called dual BRST symmetry is not an independent symmetry but the generalization of BRST symmetry obtained from the canonical transformation in the bosonic and ghost sector. We further obtain the new forms of both BRST and dual-BRST symmetry by making a general transformation in the Lagrange multipliers of the bosonic and ghost sector of the theory. © 2011 World Scientific Publishing Company.