Browsing by Author "B.P. Mandal"

Now showing 1 - 7 of 7

Absolute anticommutativity of the nilpotent symmetries in the Hamiltonian formalism: Free Abelian 2-form gauge theory
(2009) R.P. Malik; B.P. Mandal; S.K. Rai
The celebrated CurciFerrari (CF) type of restrictions are invoked to obtain the off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations in the context of the Lagrangian description of the physical four (3+1)-dimensional (4D) free Abelian 2-form gauge theory. We show that the above CF-type conditions, which turn out to be the secondary constraints of the theory, remain invariant with respect to the time-evolution of the above 2-form gauge system in the Hamiltonian formulation. This time-evolution invariance (i) physically ensures the linear independence of the BRST versus anti-BRST as well as co-BRST versus anti-co-BRST symmetry transformations, and (ii) provides a logical reason behind the imposition of the above CF-type restrictions in the proof of the absolute anticommutativity of the off-shell nilpotent (anti-)BRST as well as (anti-)co-BRST symmetry transformations. © 2009 World Scientific Publishing Company.
Augmented superfield approach to exact nilpotent symmetries for matter fields in non-Abelian theory
(2006) R.P. Malik; B.P. Mandal
We derive the nilpotent (anti-) BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4,2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x μ (with μ=0,1,2,3) and a couple of Grassmannian variables θ and θ̄. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4,1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4,2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed within the framework of augmented superfield formalism.
Knot-quiver correspondence for double twist knots
(American Physical Society, 2023) Vivek Kumar Singh; Sachin Chauhan; P. Ramadevi; Aditya Dwivedi; B.P. Mandal; Siddharth Dwivedi
We obtain a quiver representation for a family of knots called double twist knots K(p,-m). Mainly, we exploit the reverse engineering of Melvin-Morton-Rozansky formalism to deduce the pattern of the matrix for these quivers. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism
(2009) R.P. Malik; B.P. Mandal
We demonstrate that the nilpotent Becchi - Rouet - Stora - Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + l)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D space-time variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory. © Indian Academy of Sciences.
PT phase transition in a (2+1)-d relativistic system
(Academic Press Inc., 2015) B.P. Mandal; B.K. Mourya; K. Ali; A. Ghatak
We study a massless Dirac particle with PT symmetric non-Hermitian Rashba interaction in the background of Dirac oscillator potential to show the PT phase transition in a (2 + 1) dimensional relativistic system analytically. PT phase transition occurs when strength of the (i) imaginary Rashba interaction or (ii) transverse magnetic field exceed their respective critical values. Small mass gap in the spectrum, consistent with other approaches is generated as long as the system is in the unbroken phase. Relativistic Landau levels are constructed explicitly for such a system. © 2015 Elsevier Inc.
Statistical mechanics of DNA rupture: Theory and simulations
(2013) S. Nath; T. Modi; R.K. Mishra; D. Giri; B.P. Mandal; S. Kumar
We study the effects of the shear force on the rupture mechanism on a double stranded DNA. Motivated by recent experiments, we perform the atomistic simulations with explicit solvent to obtain the distributions of extension in hydrogen and covalent bonds below the rupture force. We obtain a significant difference between the atomistic simulations and the existing results in the literature based on the coarse-grained models (theory and simulations). We discuss the possible reasons and improve the coarse-grained model by incorporating the consequences of semi-microscopic details of the nucleotides in its description. The distributions obtained by the modified model (simulations and theoretical) are qualitatively similar to the one obtained using atomistic simulations. © 2013 AIP Publishing LLC.
Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields
(2009) R.P. Malik; B.P. Mandal
We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the superfields defined on a (4,2)-dimensional supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariance of the corresponding four (3+l)-dimensional (4D) Lagrangian density that describes the interaction between the U(1) gauge field and the charged complex scalar fields. The above 4D field theoretical model is considered on a (4,2)-dimensional supermanifold parametrized by the ordinary four space-time variables xμ (with μ = 0,1,2,3) and a pair of Grassmannian variables θ and θ̄ (with θ2 = θ̄2 = 0, θ2θ̄2 + θ̄2θ2 = 0). Geometrically, the (anti-)BRST invariance is encoded in the translation of the super-Lagrangian density along the Grassmannian directions of the above supermanifold such that the outcome of this shift operation is zero. © Indian Academy of Sciences.