arXiv subjects

S. Krishna

Publications and source records attributed to S. Krishna.

31 records · Page 2Linked to original sources

arXiv2015

A Free N = 2 Supersymmetric System: Novel Symmetries

We discuss a set of novel discrete symmetries of a free N = 2 supersymmetric (SUSY) quantum mechanical system which is the limiting case of a widely-studied interacting SUSY model of a charged particle constrained to move on a sphere in the background of a Dirac magnetic monopole. The usual continuous symmetries of this model provide the physical realization of the de Rham cohomological operators of differential geometry. The interplay between the novel discrete symmetries and usual continuous symmetries leads to the physical realization of relationship between the (co-)exterior derivatives of differential geometry. We have also exploited the supervariable approach to derive the nilpotent N = 2 SUSY symmetries of the theory and provided the geometrical origin and interpretation for the nilpotency property. Ultimately, our present study (based on innate symmetries) proves that our free N = 2 SUSY example is a tractable model for the Hodge theory.

hep-th↗

arXiv2015

N = 2 SUSY symmetries for a moving charged particle under influence of a magnetic field: Supervariable approach

We exploit the supersymmetric invariant restrictions (SUSYIRs) on the supervariables to derive the nilpotent N = 2 SUSY transformations for the supersymmetric quantum mechanical model of the motion of a charged particle in the X-Y plane (where the magnetic field (B_z) is applied along the Z-direction). The supervariables are defined on a (1, 2)-dimensional supermanifold parametrized by a bosonic "time" variable t and a pair of Grassmannian variables θand \barθ(with θ^2 = {\barθ}^2 = 0, θ\barθ+ \barθθ= 0). We take the (anti-)chiral supervariables for our purpose so that the nilpotency property of the N = 2 SUSY symmetry transformations could be captured within the framework of supervariable approach. We express the Lagrangian as well as supercharges in terms of the supervariables (that are obtained after the application of the appropriate SUSYIRs) and provide geometrical basis, within the framework of our supervariable approach, for (i) the nilpotency property of the above SUSY transformations, and (ii) the SUSY invariance of the Lagrangian.

hep-th↗

arXiv2014

Supervariable approach to nilpotent symmetries of a couple of N = 2 supersymmetric quantum mechanical models

We derive the on-shell as well as off-shell nilpotent supersymmetric (SUSY) symmetry transformations for the N = 2 SUSY quantum mechanical model of a one (0 + 1)-dimensional (1D) free SUSY particle by exploiting the SUSY invariant restrictions (SUSYIRs) on the (anti-)chiral supervariables of the SUSY theory that is defined on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θand \barθwith θ^2 = \barθ^2 = 0, θ\barθ+ \barθθ= 0). Within the framework of our novel approach, we express the Lagrangian and conserved SUSY charges in terms of the (anti-)chiral supervariables to demonstrate the SUSY invariance of the Lagrangian as well as the nilpotency of the SUSY conserved charges in a simple manner. Our approach has the potential to be generalized to the description of other N = 2 SUSY quantum mechanical systems with physically interesting potential functions. To corroborate the above assertion, we apply our method to derive the N = 2 continuous and nilpotent SUSY transformations for one of the simplest interacting SUSY system of a 1D harmonic oscillator.

hep-th↗

arXiv2014

Nilpotent and absolutely anticommuting symmetries in the Freedman-Townsend model: augmented superfield formalism

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations, corresponding to the (1-form) Yang-Mills (YM) and (2-form) tensorial gauge symmetries of the four (3 + 1)-dimensional (4D) Freedman-Townsend (FT) model, by exploiting the augmented version of Bonora-Tonin's (BT) superfield approach to BRST formalism where the 4D flat Minkowskian theory is generalized onto the (4, 2)-dimensional supermanifold. One of the novel observations is the fact that we are theoretically compelled to go beyond the horizontality condition (HC) to invoke an additional set of gauge-invariant restrictions (GIRs) for the derivation of the full set of proper (anti-)BRST symmetries. To obtain the (anti-)BRST symmetry transformations, corresponding to the tensorial (2-form) gauge symmetries within the framework of augmented version of BT-superfield approach, we are logically forced to modify the FT-model to incorporate an auxiliary 1-form field and the kinetic term for the antisymmetric (2-form) gauge field. This is also a new observation in our present investigation. We point out some key differences between the modified FT-model and Lahiri-model (LM) of the dynamical non-Abelian 2-form gauge theories.

hep-th↗

arXiv2014

General N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach to its Off-Shell Nilpotent Symmetries

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0 + 1)-dimensional N = 2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θand \barθwith θ^2 = \barθ^2 = 0, θ\barθ+ \barθθ= 0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSY invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N = 2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations.

hep-th↗

arXiv2014

Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory

Taking the simple examples of an Abelian 1-form gauge theory in two (1 + 1)-dimensions, a 2-form gauge theory in four (3 + 1)-dimensions and a 3-form gauge theory in six (5 + 1)-dimensions of spacetime, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p (p = 1, 2, 3,...) dimensions of spacetime. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5 + 1)-dimensions of spacetime, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.

hep-th↗

arXiv2013

A novel observation in the BRST approach to a free spinning relativistic particle

For the newly proposed coupled (but equivalent) Lagrangians for the supersymmetric (SUSY) system of a one (0 + 1)-dimensional spinning relativistic particle, we derive the Noether conserved charges corresponding to its (super)gauge, Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and ghost-scale symmetry transformations. We deduce the underlying algebra amongst the continuous symmetry operators and corresponding conserved charges. We point out a novel observation that emerges, for this specific SUSY system, when we discuss it within the framework of BRST formalism. In particular, the requirement of the physicality criteria with the (anti-)BRST charges leads to a completely new observation because, as it turns out, one of the primary constraints does not annihilate the physical state of the theory. We have never come across this kind of result in the realm of BRST approach to usual gauge theories. We provide the physical and theoretical reasons behind the above observation.

hep-th↗

arXiv2012

Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (τ) and a pair of odd (fermionic) variables θand \barθ(with θ^2 = \barθ^2 = 0,\; θ\barθ+ \barθθ= 0) of the Grassmann algebra. One of the most important features of our present investigation is the derivation of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST symmetry transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system.

hep-th↗

arXiv2012

Dual-BRST symmetry: 6D Abelian 3-form gauge theory

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5 + 1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.

hep-th↗

arXiv2011

Comments on the dual-BRST symmetry

In view of a raging controversy on the topic of dual-Becchi-Rouet-Stora-Tyutin (dual-BRST/co-BRST) and anti-co-BRST symmetry transformations in the context of four (3+1)-dimensional (4D) Abelian 2-form and 2D (non-)Abelian 1-form gauge theories, we attempt, in our present short note, to settle the dust by taking the help of mathematics of differential geometry, connected with the Hodge theory, which was the original motivation for the nomenclature of "dual-BRST symmetry" in our earlier set of works. It has been claimed, in a recent set of papers, that the co-BRST symmetries are not independent of the BRST symmetries. We show that the BRST and co-BRST symmetries are independent symmetries in the same fashion as the exterior and co-exterior derivatives are independent entities belonging to the set of de Rham cohomological operators of differential geometry.

hep-th↗

arXiv2011

Topologically massive non-Abelian theory: superfield formalism

We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3 + 1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-) BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-) BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-) BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-) BRST symmetry transformations when the (anti-) BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-) BRST symmetries are, however, found to be not absolutely anticommuting in nature.

hep-th↗

arXiv2007

Oscillations and temporal signalling in cells

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration, using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show "ultradian" oscillations, with time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NFkB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.

q-bio.MN↗

arXiv1998

Tests of Dynamical Scaling in 3-D Spinodal Decomposition

We simulate late-stage coarsening of a 3-D symmetric binary fluid. With reduced units l,t (with scales set by viscosity, density and surface tension) our data extends two decades in t beyond earlier work. Across at least four decades, our own and others' individual datasets (< 1 decade each) show viscous hydrodynamic scaling (l ~ a + b t), but b is not constant between runs as this scaling demands. This betrays either the unexpected intrusion of a discretization (or molecular) lengthscale, or an exceptionally slow crossover between viscous and inertial regimes.

cond-mat.soft↗