arXiv subjects

N. Srinivas

Publications and source records attributed to N. Srinivas.

10 recordsLinked to original sources

arXiv2021

Thermodynamics of Bosonic Higher Spin Fields

In this paper, I calculated the partition function of the quantum statistical system of free massless bosonic Higher spin (HS) fields on $d$-dimensional Minkowski spacetime by using the Feynman's path integral approach, it is a nontrivial result and this explain about the self-duality between the Quantum statistical system of massless free bosonic HS fields of $s \geq 2$ over $d \geq 4$ dimensional Minkowski spacetime and the Quantum statistical system of Klein-Gordon bosonic (scalar) fields on 4-dimensional Minkowski spacetime at the thermal equilibrium. However, I have been used the dimensional regularization method to calculate the free energy of this system in this calculations the ultraviolet divergences(UV) present that could be eliminated. Nevertheless, still have infrared (IR) divergences in this theory and also I discussed about the average energy and the entropy of this system over $d \geq 4$-dimensional Minkowski spacetime. In particular,the most significant result is that the average energy spectrum of quantum statistical system of massless bosonic HS fields is similar to the blackbody radiation energy spectrum at different temperatures and also it explain the Universe cosmic microwave background(CMB)radiation spectrum (COBE data) at 2.7 kelvin temperature. However, the entropy of massless free bosonic HS fields also explain the self duality between the massless free bosonic HS fields and Klein-Gordon bosonic (scalar) fields over 4-dimensional Minkowski spacetime.

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arXiv2019

Nilpotent Charges of a Toy Model of Hodge Theory and an ${\cal N}$ = $2$ SUSY Quantum Mechanical Model: (Anti-)Chiral Supervariable Approach

We derive the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for the system of a toy model of Hodge theory (i.e. a rigid rotor) by exploiting the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral supervariables that are defined on the appropriately chosen (1, 1)-dimensional super-submanifolds of the {\it general} (1, 2)-dimensional supermanifold on which our system of a one (0 + 1)-dimensional (1D) toy model of Hodge theory is considered within the framework of the augmented version of the (anti-)chiral supervariable approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism. The general (1, 2)-dimensional supermanifold is parameterized by the superspace coordinates ($t, θ, \barθ$) where $t$ is the bosonic evolution parameter and ($θ, \barθ$) are the Grassmannian variables which obey the standard fermionic relationships: $ θ^2 = {\barθ}^2 = 0, θ\,{\barθ} + {\barθ}\,θ = 0 $. We provide the geometrical interpretations for the symmetry invariance and nilpotency property. Furthermore, in our present endeavor, we establish the property of absolute anticommutativity of the conserved fermionic charges which is a completely {\it novel} and surprising observation in our present endeavor where we have considered {\it only} the (anti-)chiral supervariables. To corroborate the {\it novelty} of the above observation, we apply this ACSA to an ${\cal N} = 2$ SUSY quantum mechanical (QM) system of a free particle and show that the ${\cal N} = 2$ SUSY conserved and nilpotent charges do {\it not} absolutely anticommute.

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arXiv2018

Nilpotent Symmetries of a 4D Model of the Hodge Theory: Augmented (Anti-)Chiral Superfield Formalism

We derive the continuous nilpotent symmetries of the four (3 + 1)-dimensional (4D) model of the Hodge theory (i.e. 4D Abelian 2-form gauge theory) by exploiting the beauty and strength of the symmetry invariant restrictions on the (anti-)chiral superfields. The above off-shell nilpotent symmetries are the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST transformations which turn up beautifully due to the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral superfields that are defined on the (4, 1)-dimensional (anti-)chiral super-submanifolds of the general (4, 2)-dimensional supermanifold on which our ordinary 4D theory is generalized. The latter supermanifold is characterized by the superspace coordinates $Z^M = (x^μ,\, θ,\, \barθ)$ where $x^μ\, (μ= 0, 1, 2, 3 )$ are the bosonic coordinates and a pair of Grassmannian variables $θ$ and $\barθ$ are fermionic in nature as they obey the standard relationships: $θ^2 = {\barθ}^2 = 0,\, θ\,\barθ+ \barθ\,θ= 0$). The derivation of the {\it proper} (anti-)co-BRST symmetries and proof of the absolute anticommutativity property of the conserved (anti-)BRST and (anti-) co-BRST charges are novel results of our present investigation (where only the (anti-)chiral superfields and their super-expansions have been taken into account).

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arXiv2017

Nilpotent Symmetries and Curci-Ferrari Type Restrictions in 2D Non-Abelian Gauge Theory: Superfield Approach

We derive the off-shell nilpotent symmetries of the two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF) type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parameterized by the superspace coordinates Z^{M} = (x^μ, θ, \barθ) where x^{μ} (with μ= 0,1) are the bosonic coordinates and a pair of Grassmannian variables (θ, \barθ) obey the relationships: θ^{2} = \barθ^{2} = 0, θ\barθ+ \barθθ= 0.

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arXiv2017

Some Novel Features in 2D Non-Abelian Theory: BRST Approach

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF) type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.

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arXiv2017

Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism

We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator (and its Hermitian conjugate) and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor, modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual-horizontality condition (DHC) and dual-gauge invariant restrictions (DGIRs) of the superfield formalism. The derivation of the dual unitary operators and corresponding (anti-)dual BRST symmetries are completely novel results in our present investigation.

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arXiv2017

(Anti-)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory

We exploit the beauty and strength of the symmetry invariant restrictions on the (anti-)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations in the case of a two (1+1)-dimensional (2D) self-dual chiral bosonic field theory within the framework of augmented (anti-)chiral superfield formalism. Our 2D ordinary theory is generalized onto a (2, 2)-dimensional supermanifold which is parameterized by the superspace variable Z^M = (x^μ, θ, \barθ) where x^μ(with μ= 0, 1) are the ordinary 2D bosonic coordinates and (θ,\, \barθ) are a pair of Grassmannian variables with their standard relationships: θ^2 = {\barθ}^2 =0, θ\,\barθ+ \barθθ= 0. We impose the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral superfields (defined on the (anti-)chiral (2, 1)-dimensional super-submanifolds of the above general (2, 2)-dimensional supermanifold) to derive the above nilpotent symmetries. We do not exploit the mathematical strength of the (dual-)horizontality conditions anywhere in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity and (anti-)BRST and (anti-)co-BRST symmetry invariance of the Lagrangian density within the framework of our augmented (anti-)chiral superfield formalism. Our observation of the absolute anticommutativity property is a completely novel result in view of the fact that we have considered only the (anti-)chiral superfields in our present endeavor.

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arXiv2016

Universal Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach

Within the framework of augmented version of superfield formalism, we derive the superspace unitary operator and show its usefulness in the derivation of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a set of interesting models for the Abelian 1-form gauge theories. These models are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two (1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian 1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory. We provide, in some sense, the alternatives to the horizontality condition (HC) and the gauge invariant restrictions (GIRs) in the language of the above superspace (SUSP) unitary operator. One of the key observations of our present endeavor is the result that the SUSP unitary operator and its hermitian conjugate are found to be the same for all the Abelian models under consideration (including the 4D interacting Abelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier). Thus, we establish the universality of the SUSP operator for the above Abelian theories.

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arXiv2015

N = 2 Supersymmetric Harmonic Oscillator: Basic Brackets Without Canonical Conjugate Momenta

We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) N = 2 supersymmetric (SUSY) harmonic oscillator (HO) without taking the help of the mathematical definition of canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory provide the physical realizations of the de Rham cohomological operators of differential geometry). In our present endeavor, it is the full set of continuous symmetries and their corresponding generators that lead to the derivation of basic (anti)commutators amongst the creation and annihilation operators that appear in the normal mode expansions of the dynamical fermionic and bosonic variables of our present N = 2 SUSY theory of a HO. These basic brackets are in complete agreement with such kind of brackets that are derived from the standard canonical method of quantization scheme.

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arXiv2011

$κ$-deformed Dirac Equation

We construct a Dirac equation in $κ$-Minkowski spacetime and analyse its implications. This $κ$-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, $a$. We show that the $κ$-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the Hydrogen atom spectrum is modified due to the $κ$-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter $a$, which are few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.

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