arXiv subjects

T. R. Govindarajan

Publications and source records attributed to T. R. Govindarajan.

At least 19 recordsLinked to original sources

arXiv2026

Time-dependent Magnetic Fields and the Quantum Hall Effect

Ermakov has shown how the solution to the classical harmonic oscillator in one spatial dimension with general time-dependent frequency can be reduced to the time-independent case and an associated nonlinear ordinary differential equation, an analysis which has been applied to the Schrödinger equation as well. We extend this analysis to the Landau problem of a charged particle in a uniform magnetic field in two dimensions and construct the generalized Laughlin wave functions for the case when the magnetic field is time-dependent. We also work out the dynamics of density fluctuations (the Girvin, MacDonald, Platzman or GMP mode) and argue that it is possible to tune the frequency of the magnetic field to obtain a compressible droplet of fermions. We also analyze the dynamics of the edge modes of the droplet for the integer Hall effect.

cond-mat.mes-hall↗

arXiv2025

Over-Luminous Type Ia Supernovae and Standard Candle Cosmology

Type Ia supernovae (SNe\,Ia) serve as crucial cosmological distance indicators because of their empirical consistency in peak luminosity and characteristic light curve decline rates. These properties facilitate them to be standardized candles for the determination of the Hubble constant ($H_0$) within late-time universe cosmology. Nevertheless, a statistically significant difference persists between $H_0$ values derived from early and late-time measurements, a phenomenon known as the Hubble tension. Furthermore, recent observations have identified a subset of over-luminous SNe\,Ia, characterized by peak luminosities exceeding the nominal range and faster decline rates. These discoveries raise questions regarding the reliability of SNe\,Ia as standard candles for measuring cosmological distances. In this article, we present the Bayesian analysis of 15 over-luminous SNe\,Ia and show that they yield a lower $H_0$ estimate due to the increase in their absolute magnitude. This investigation potentially represents a step toward addressing the Hubble tension.

astro-ph.CO↗

arXiv2025

Generalized Landau Yang Theorem

Landau Yang theorem is well known for the past several decades. It prohibits the decay of a massive spin 1 particle to two photons. This emerges simply from the representation theory of the Poincare group and Bose Statistics. It does not require any action or Lagrangian. We generalize this theorem to theories with supersymmetry (SUSY) which disallows even decay to two photinos (Majorana fermions) as well as the decay of a zino to a photon and a photino. We will prove that if the photon has a mass, howsoever small, this theorem can be evaded. We also show that the supersymmetric selection rule above can also be evaded through the Stueckelberg mass term. Further interesting implications are also pointed out.

hep-th↗

arXiv2021

Natural evidence for fuzzy sphere noncommutative geometry: super-Chandrasekhar white dwarfs

Noncommutative geometry is one of the quantum gravity theories, which various researchers have been using to describe different physical and astrophysical systems. However, so far, no direct observations can justify its existence, and this theory remains a hypothesis. On the other hand, over the past two decades, more than a dozen over-luminous type Ia supernovae have been observed, which indirectly predict that they originate from white dwarfs with super-Chandrasekhar masses $2.1-2.8 \rm\,M_\odot$. In this article, we discuss that considering white dwarfs as squashed fuzzy spheres, a class of noncommutative geometry, helps in accumulating more mass than the Chandrasekhar mass-limit. The length-scale beyond which the effect of noncommutativity becomes prominent is an emergent phenomenon, which depends only on the inter-electron separations in the white dwarf.

gr-qc↗

arXiv2021

Super-Chandrasekhar limiting mass white dwarfs as emergent phenomena of noncommutative squashed fuzzy spheres

The indirect evidence for at least a dozen massive white dwarfs violating the Chandrasekhar mass-limit is considered to be one of the wonderful discoveries in astronomy for more than a decade. Researchers have already proposed a diverse amount of models to explain this astounding phenomenon. However, each of these models always carries some drawbacks. On the other hand, noncommutative geometry is one of the best replicas of quantum gravity, which is yet to be proved from observations. Madore introduced the idea of a fuzzy sphere to describe a formalism of noncommutative geometry. This article shows that the idea of a squashed fuzzy sphere can self-consistently explain the super-Chandrasekhar limiting mass white dwarfs. We further show that the length-scale beyond which the noncommutativity is prominent is an emergent phenomenon, and there is no prerequisite for an ad-hoc length-scale.

gr-qc↗

arXiv2021

Significantly super-Chandrasekhar mass-limit of white dwarfs in noncommutative geometry

Chandrasekhar made the startling discovery about nine decades back that the mass of compact object white dwarf has a limiting value, once nuclear fusion reactions stop therein. This is the Chandrasekhar mass-limit, which is $\sim1.4M_\odot$ for a non-rotating non-magnetized white dwarf. On approaching this limiting mass, a white dwarf is believed to spark off with an explosion called type Ia supernova, which is considered to be a standard candle. However, observations of several over-luminous, peculiar type Ia supernovae indicate that the Chandrasekhar mass-limit to be significantly larger. By considering noncommutativity among the components of position and momentum variables, hence uncertainty in their measurements, at the quantum scales, we show that the mass of white dwarfs could be significantly super-Chandrasekhar and thereby arrive at a new mass-limit $\sim 2.6M_\odot$, explaining a possible origin of over-luminous peculiar type Ia supernovae. The idea of noncommutativity, apart from the Heisenberg's uncertainty principle, is there for quite sometime, without any observational proof however. Our finding offers a plausible astrophysical evidence of noncommutativity, arguing for a possible second standard candle, which has many far-reaching implications.

gr-qc↗

arXiv2020

Stuckelberg SUSY QED and Infrared Problem

We review gauge invariant $\mathcal N =1$ supersymmetric massive $U(1)$ gauge theory coupled to matter and Stuckelberg superfields. We focus on the leading order self energy and vertex correction to the matter field in the massless limit of both the $U(1)$ vector superfield and the Stuckelberg superfield. We explicitly verify that the theory is infrared divergence free in the massless limit. Hence the Stuckelberg mechanism appears to be the efficient route to handle infrared divergences seen in supersymmetric quantum electrodynamics.Since these additional particles have very small masses they can serve as dark matter candidates through `Ultralight particles' mechanism.

hep-th↗

arXiv2019

Embedding into flat spacetime and black hole thermodynamics

It is known that static and spherically symmetric black hole solutions of general relativity in different spacetimes can be embedded into higher dimensional flat spacetime. Given this result, we have explored the thermodynamic nature of black holes á la its embedding into flat spacetime. In particular, we have explicitly demonstrated that black hole temperature can indeed be determined starting from the embedding and hence mapping of the static observers in black hole spacetime to Rindler observers in flat spacetime. Furthermore, by considering the dynamics of a scalar field in the flat spacetime it is indeed possible to arrive at the area scaling law for black hole entropy. Thus using flat spacetime field theory, one can indeed provide a thermodynamic description of black holes. Implications are also discussed.

gr-qc↗

arXiv2019

Stueckelberg Bosons as an Ultralight Dark Matter Candidate

In this letter, we propose a new model of fuzzy dark matter based on Stueckelberg theory. Dark matter is treated as a Bose-Einstein condensate of Stueckelberg particles and the resulting cosmological effects are analyzed. Fits are understood for the density and halo sizes of such particles and comparison with existing models is made. Certain attractive properties of the model are demonstrated and lines for future work are laid out.

hep-ph↗

arXiv2019

Light front QED, Stueckelberg field and Infrared divergence

Stueckelberg mechanism introduces a scalar field, known as Stueckelberg field, so that gauge symmetry is preserved in the massive abelian gauge theory. In this work, we show that the role of the Stueckelberg field is similar to the Kulish and Faddeev coherent state approach to handle infrared (IR) divergences. We expect that the light-front quantum electrodynamics (LFQED) with Stueckelberg field must be IR finite in the massless limit of the gauge boson. We have explicitly shown the cancellation of IR divergences in the relevant diagrams contributing to self-energy and vertex correction at leading order.

hep-th↗

arXiv2016

Modelling quantum black hole

Novel bound states are obtained for manifolds with singular potentials. These singular potentials require proper boundary conditions across boundaries. The number of bound states match nicely with what we would expect for black holes. Also they serve to model membrane mechanism for the black hole horizons in simpler contexts. The singular potentials can also mimic expanding boundaries elegantly, there by obtaining appropriately tuned radiation rates.

hep-th↗

arXiv2015

Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.

hep-th↗

arXiv2013

Quantum field theories with boundaries and novel instabilities

Quantum physics on manifolds with boundary brings novel aspects due to boundary conditions. One important feature is the appearance of localised negative eigenmodes for the Laplacian on the boundary. These can potentially lead to instabilities. We consider quantum field theories on such manifolds and interpret these as leading to the onset of phase transitions.

hep-th↗

arXiv2013

Algebraic Approach to Entanglement and Entropy

We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation space of the observable algebra, once a state is chosen. In this approach, which is based on the Gelfand-Naimark-Segal construction, the study of subsystems becomes particularly clear. We explicitly show how the problems associated with partial trace for the study of entanglement of identical particles are readily overcome. In particular, a suitable entanglement measure is proposed, that can be applied to systems of particles obeying Fermi, Bose, para- and even braid group statistics. The generality of the method is also illustrated by the study of time evolution of subsystems emerging from restriction to subalgebras. Also, problems related to anomalies and quantum epistemology are discussed.

math-ph↗

arXiv2012

Twisted bosonization in two dimensional noncommutative spacetime

We study the twisted bosonization of massive Thirring model to relate to sine-Gordon model in Moyal spacetime using twisted commutation relations. We obtain the relevant twisted bosonization rules. We show that there exists dual rela- tionship between twisted bosonic and fermionic operators. The strong-weak duality is also observed to be preserved as its commutative counterpart.

hep-th↗

arXiv2012

Entanglement, Particle Identity and the GNS Construction: A Unifying Approach

A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from pure ones based on taking partial traces is replaced by the more general notion of the restriction of a state to a subalgebra. For bipartite systems of nonidentical particles, this approach reproduces the standard results. But it also very naturally overcomes the limitations of the usual treatment of systems of identical particles. This GNS approach seems very general and can be applied for example to systems obeying para- and braid- statistics including anyons.

quant-ph↗

arXiv2012

Electric Dipole Moment from QCD $θ$ and How It Vanishes for Mixed States

In a previous paper [1], we studied the $η'$ mass and formulated its chirally symmetric coupling to fermions which induces electric dipole moment (EDM). Here we calculate the EDM to one-loop. It is finite, having no ultraviolet divergence while its infrared divergence is canceled by soft photon emission processes \emph{exactly} as for $θ=0$. The coupling does not lead to new divergences (not present for $\sinθ=0$) in soft photon processes either. Furthermore, as it was argued previously [1], the EDM vanishes if suitable mixed quantum states are used. This means that in a quantum theory based on such mixed states, a strong bound on EDM will not necessarily lead to a strong bound such as $|\sin θ|\lesssim 10^{-11}$ . This fact eliminates the need to fine-tune $θ$ or for the axion field.

hep-th↗

arXiv2012

Novel Studies on the η' Effective Lagrangian

The effective Lagrangian for η' incorporating the effect of the QCD θ-angle has been developed previously. We revisit this Lagrangian and carry out its canonical quantization with particular attention to the test function spaces of constraints and the topology of the η'-field. In this way, we discover a new chirally symmetric coupling of this field to chiral multiplets which involves in particular fermions. This coupling violates P and T symmetries. In a subsequent paper, we will evaluate its contribution to the electric dipole moment (EDM) of fermions. Our motivation is to test whether the use of mixed states restores P and T invariance, so that EDM vanishes. This calculation will be shown to have striking new physical consequences.

hep-ph↗