Dr. Vipul Kumar Pandey
Verified @gmail.com
Scopus Publications
- Connecting Green’s functions in the Siegel-Zwiebach model through FFBRST transformations
Vipul Kumar Pandey, Ronaldo Thibes
Nuclear Physics B, 2026 - On Lagrangian Formulations for (Ir)Reducible Mixed-Antisymmetric Higher Integer Spin Fields in Minkowski Spaces
Alexander A. Reshetnyak, Julia V. Bogdanova, Vipul K. Pandey
Moscow University Physics Bulletin, 2025
We extend the results of Lagrangian formulations study to construct gauge-invariant Lagrangians for (ir)reducible integer higher-spin massless and massive representations of the Poincare group with a Young tableau $Y[\hat{s}_1,\hat{s}_2,\hat{s}_3]$ in $d$-dimensional flat space-time (as the probable candidates to describe the Dark Matter problem beyond the SM). These particles are described within a metric-like formulation by tensor fields with 3 groups of antisymmetric Lorentz indices $Φ_{μ^1[{\hat{s}_1}],μ^2[{\hat{s}_2}], μ^3[{\hat{s}_3}]}$ on a basis of the BRST method with complete, $Q$, and incomplete, $Q_c$, BRST operators. We found unconstrained (with $Q$) and constrained (with $Q_c$ and off-shell BRST invariant holonomic constraints) gauge Lagrangian formulations with different configuration spaces and reducibility stages. The deformation procedure to construct interacting gauge model with mixed-antisymmetric fields is proposed. - Functional BRST-invariant approach to the Siegel-Zwiebach symmetric rank-two tensor action in the critical dimension – massive gravity clues from string theory
Vipul Kumar Pandey, Ronaldo Thibes
Nuclear Physics B, 2025
We discuss the rank-two tensorial Siegel-Zwiebach action from string field theory within a BRST-invariant functional framework in the bosonic critical dimension. We obtain a new family of generalized proper gauge-fixing conditions. Gauge attainability and all corresponding nillpotent BRST symmetries are explicitly worked out. Finite-field-dependent BRST transformations (FFBRST) are shown to connect the effective ghost-dependent actions in different gauges. The massive Fierz-Pauli Lagrangian can be obtained from the gauge-invariant Siegel-Zwiebach one in the unitary gauge as a particular case, however, due to the well-known van Dam-Veltman-Zakharov (vDVZ) discontinuity, possessing a ill-defined propagator in the massless limit. Nevertheless, alternatively working in a more suitable generalized Lorenz type gauge, including the transverse-traceless case, the graviton propagator within the Siegel-Zwiebach Lagrangian context can be made finite in the massless limit. We write down the complete Green's functions generating functional, including the auxiliary fields and ghosts sectors. By taking into account the corresponding change in the Feynman integral Jacobian, we construct a convenient FFBRST transformation connecting the unitary gauge to a new bi-parametrized class of gauge-fixings containing the transverse-traceless case. - Symplectic quantization and general constraint structure of a prototypical second-class system
Ignacio S. Gomez, Vipul Kumar Pandey, Ronaldo Thibes
European Physical Journal C, 2024
We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical model amounts to a Dirac–Bergmann singular system, whose constraints restrict the actual dynamics to occur within a differential submanifold, as is the case in the major part of field theoretical models with gauge symmetry. We apply the Dirac–Bergmann algorithm in its full generality unraveling a total of 4m second-class constraints and obtain the corresponding Dirac brackets algebra in phase space. We follow with the Faddeev–Jackiw–Barcelos–Wotzasek approach in which the geometric character of the mentioned submanifold is emphasized by means of an internal metric function encoding its symplectic properties. We consider two straightforward examples, applying our general results to constrained motion along a toroidal geometry and to a Lorentz violating toy model in field theory. Since toroidal geometry has been recently used in cosmological models, we suggest how our results could lead to different proposals for the shape of the universe in cosmology. - Geometric Quantization of a Constrained System
Vipul Kumar Pandey
Springer Proceedings in Physics, 2024 - BFV quantization and BRST symmetries of the gauge invariant fourth-order Pais-Uhlenbeck oscillator
Bhabani Prasad Mandal, Vipul Kumar Pandey, Ronaldo Thibes
Nuclear Physics B, 2022
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. - A prototypical nonlinear second-class system and its BFFT constraints Abelianization
V. K. Pandey, R. Thibes
Modern Physics Letters A, 2022
We apply the Batalin–Fradkin–Fradkina–Tyutin formalism to a prototypical second-class system, aiming to convert its constraints from second class to first class. The proposed system admits a consistent initial set of second-class constraints and an open potential function providing room for feasible applications to field theory and mechanical models. The constraints can be arbitrarily nonlinear, broadly generalizing previously known cases. We obtain a sufficient condition for which a simple closed expression for the Abelian converted constraints and modified involutive Hamiltonian can be achieved. As an explicit example, we discuss a spontaneous Lorentz symmetry breaking vectorial model, obtaining the full first-class Abelianized constraints in closed form and the corresponding involutive Hamiltonian. - Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold II
Vipul Kumar Pandey
Advances in High Energy Physics, 2022
We have previously developed the BRST quantization on the hypersurface V N − 1 embedded in N -dimensional Euclidean space R N in both Hamiltonian and Lagrangian formulation. We generalize the formalism in the case of L -dimensional manifold V L embedded in R N with 1 ≤ L < N . The result is essentially the same as the previous one. We have also verified the results obtained here using a simple example of particle motion on a torus knot. - Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold
V. Pandey
Advances in High Energy Physics, 2022
The BRST quantization of particle motion on the hypersurface V N − 1 embedded in Euclidean space R N is carried out both in Hamiltonian and Lagrangian formalism. Using Batalin-Fradkin-Fradkina-Tyutin (BFFT) method, the second class constraints obtained using Hamiltonian analysis are converted into first class constraints. Then using BFV analysis the BRST symmetry is constructed. We have given a simple example of these kind of system. In the end we have discussed Batalin-Vilkovisky formalism in the context of this (BFFT modified) system. - BRST-BFV and BRST-BV descriptions for bosonic fields with continuous spin on R 1, d - 1
Č. Burdík, V. K. Pandey, A. Reshetnyak
International Journal of Modern Physics A, 2020
Gauge-invariant descriptions for a free bosonic scalar field of continuous spin in a [Formula: see text]-dimensional Minkowski space–time using a metric-like formulation are constructed on the basis of a constrained BRST–BFV approach we propose. The resulting BRST–BFV equations of motion for a scalar field augmented by ghost operators contain different sets of auxiliary fields, depending on the manner of a partial gauge-fixing and a resolution of some of the equations of motion for a BRST-unfolded first-stage reducible gauge theory. To achieve an equivalence of the resulting BRST-unfolded constrained equations of motion with the initial irreducible Poincaré group conditions of a Bargmann–Wigner type, it is demonstrated that one should replace the field in these conditions by a class of gauge-equivalent configurations. Triplet-like, doublet-like constrained descriptions, as well as an unconstrained quartet-like non-Lagrangian and Lagrangian formulations, are derived using both Fronsdal-like and new tensor fields. In particular, the BRST–BV equations of motion and Lagrangian using an appropriate set of Lagrangian multipliers in the minimal sector of the respective field and antifield configurations are constructed in a manifest way. - Conformal to harmonic gauge for bosonic strings
Vipul Kumar Pandey, Bhabani Prasad Mandal
Epl, 2019 - Weyl degree of freedom in the Nambu-Goto string through field transformation
Vipul Kumar Pandey, Bhabani Prasad Mandal
Epl, 2018 - BRST Qantization on Torus Knot
Vipul Kumar Pandey, Bhabani Prasad Mandal
Springer Proceedings in Physics, 2018 - BRST symmetry for a torus knot
Vipul Kumar Pandey, Bhabani Prasad Mandal
Epl, 2017 - Double Hodge Theory for a Particle on Torus
Vipul Kumar Pandey, Bhabani Prasad Mandal
Advances in High Energy Physics, 2017 - Maximal Abelian gauge and a generalized BRST transformation
Shinichi Deguchi, Vipul Kumar Pandey, Bhabani Prasad Mandal
Physics Letters Section B Nuclear Elementary Particle and High Energy Physics, 2016
