arXiv subjects

Amitabha Lahiri

Publications and source records attributed to Amitabha Lahiri.

At least 37 records · Page 2Linked to original sources

arXiv2022

Discrete symmetry transformations on non-abelian gauge fields

All gauge bosons of a non-abelian gauge theory do not transform the same way under the discrete transformations of time-reversal and charge-conjugation. Moreover, the transformations rules depend on how the generators are chosen. We show how well-defined rules pertain only to specific choices of generators, and then show how unified rules can be constructed, using matrix forms of the gauge bosons, which are completely independent of the choice of generators.

hep-th↗

arXiv2022

Bianchi-I cosmology in quantum gravity

The exact renormalization group flow equations for gravity lead to quantum corrections of Newton's constant and cosmological constant. Using this we investigate the Bianchi-I cosmological model at late times. In particular, we obtain the scale factors in different directions, and observe that they eventually evolve into Friedmann-Lemaître-Robertson-Walker (FLRW) universe for radiation. However, for stiff matter the universe shows a Kasner like behaviour. The presentation is based on our work published in \cite{Mandal:2019xlg}.

gr-qc↗

arXiv2022

Spin-flux attachment by dimensional reduction of vortices

The description of a system of vortices in terms of dual fields provides a window to new phases of the system. It was found recently that dualizing a 3+1-d boson-fermion system leads to a system of fermions and vortices interacting via a 2-form field through a non-local term. Here we explore some consequences of such an interaction when the degrees of freedom of the system are confined to a 2+1-d space-time. In particular, we show that the vortices in the 2+1-d system are attached to the fermions via their non-zero spin magnetic moment in a way similar to the phenomenon of flux attachment in Chern-Simons gauge theory coupled to matter. We also show that such flux attached particles exhibit fractional statistical behaviour like anyons. Thus our model provides a realization of anyons without Chern-Simons theory.

hep-th↗

arXiv2022

Scalar-Fermion Interaction as the Driver of Cosmic Acceleration

We argue that an interacting scalar-fermion distribution can be used to demonstrate the cosmic acceleration in General Relativity. The interaction is of Yukawa nature and it drives the fermion density to decay with cosmic time. The consistency of the model is established through, (a) a generalization of the Om(z) parameter, the present matter density contrast of the universe, and (b) a comparison of theoretical results with observational data, using a Markov Chain Monte Carlo code. A simple model of unified cosmic expansion history is also discussed. There are more than one instances where the universe goes through a transition between subsequent epochs with different patterns of cosmic expansion. These patterns impose some constraints on the scalar-fermion interaction profile and on the overall cosmological dynamics.

gr-qc↗

arXiv2022

Spin gauge theory, duality and fermion pairing

We apply duality transformation to the Abelian Higgs model in 3+1 dimensions in the presence of electrons coupled to the gauge field. The Higgs field is in the symmetry broken phase, where flux strings can form. Dualization brings in an antisymmetric tensor potential $B_{μν}\,$, which couples to the electrons through a nonlocal interaction which can be interpreted as a coupling to the spin current. It also couples to the string worldsheet and gives rise to a string Higgs mechanism via the condensation of flux strings. In the phase where the $B_{μν}$ field is massless, the nonlocal interaction implies a linearly rising attractive force between the electrons, which can be interpreted as the result of a pair of strings joining the electrons.

hep-th↗

arXiv2021

Cosmology with modified continuity equation in asymptotically safe gravity

We study FLRW cosmology, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective action for gravity. We calculate the quantum corrected scale factor, energy density, and entropy production at late times, taking different cut-off functions. Our approach differs from previous ones in the way energy-momentum conservation is imposed -- we include the running Newton constant $G(k)$ in the definition of energy-momentum tensor, keeping in mind the covariant conservation identity of the Einstein tensor. The quantum corrections obtained in this approach are different from what are found by letting the conservation equation remain the same as for a scale-independent Newton constant. We also find that for a specific choice of the cut-off scale, the quantum corrected behaviour of the Newton constant and the cosmological constant lead to a bouncing emergent universe solution.

gr-qc↗

arXiv2020

Pushforwards and Gauge Transformations for Categorical Connections

We construct and study pushforwards of categorical connections on categorical principal bundles. Applying this construction to the case of decorated path spaces in principal bundles, we obtain a transformation of classical connections that combines the traditional gauge transformation with an affine translation.

math.DG↗

arXiv2020

Geometry creates inertia

The dynamics of fermions in curved spacetime is governed by a spin connection, a part of which is contorsion, an auxiliary field independent of the metric, without dynamics but fully expressible in terms of the axial current density of fermions. Its effect is the appearance of a quartic interaction involving all fermions. Contorsion can couple to left and right-handed fermions with different strengths, leading to an effective mass for fermions propagating on a background containing fermionic matter.

gr-qc↗

arXiv2020

Emergent vortex-electron interaction from dualization

We consider the Abelian Higgs model in 3+1 dimensions with vortex lines, into which charged fermions are introduced. This could be viewed as a model of a type-II superconductor with unpaired electrons (or holes), analogous to the boson-fermion model of high-$T_c$ superconductors but one in which the bosons and fermions interact only through the electromagnetic gauge field. We investigate the dual formulation of this model, which is in terms of a massive antisymmetric tensor gauge field $B_{μν}$ mediating the interaction of the vortex lines. This field couples to the fermions through a nonlocal spin-gauge interaction term. We then calculate the quantum correction due to the fermions at one loop and show that due to the presence of this new nonlocal term a topological $B \wedge F$ interaction is induced in the effective action, leading to an increase in the mass of both the photon and the tensor gauge field. Additionally, we find a Coulomb potential between the electrons, but with a large dielectric constant generated by the one-loop effects.

hep-th↗

arXiv2020

Cosmology of Bianchi type-I metric using renormalization group approach for quantum gravity

We study the anisotropic Bianchi type-I cosmological model at late times, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective average action for gravity. The cosmological evolution equations are derived by including the scale dependence of Newton's constant $G$ and cosmological constant $Λ$. We have considered the solutions of the flow equations for $G$ and $Λ$ at next to leading order in the infrared cutoff scale. Using these scale dependent $G$ and $Λ$ in Einstein equations for the Bianchi-I model, we obtain the scale factors in different directions. It is shown that the scale factors eventually evolve into FLRW universe for known matter like radiation. However, for dust and stiff matter we find that the universe need not evolve to the FLRW cosmology in general, but can also show Kasner type behaviour.

gr-qc↗

arXiv2019

Geometrical contribution to neutrino mass matrix

The dynamics of fermions on curved spacetime requires a spin connection, which contains a part called contorsion, an auxiliary field without dynamics but fully expressible in terms of the axial current density of fermions. Its effect is the appearance of a quartic interaction of all fermions in the action, leading to a nonlinear Dirac equation involving all fermions present. Noting that left and right-chiral fermions may couple to contorsion by different strengths, we show that all fermions gain an effective mass when propagating through fermionic matter. This may have an observable effect on neutrino oscillations. In particular we find that different neutrino flavors can mix even if they have zero rest mass in vacuum, without requiring fields beyond the Standard Model.

hep-ph↗

arXiv2019

Different types of torsion and their effect on the dynamics of fields

One of the formalisms that introduces torsion conveniently in gravity is the vierbein-Einstein-Palatini (VEP) formalism. The independent variables are the vierbein (tetrads) and the components of the spin connection. The latter can be eliminated in favor of the tetrads using the equations of motion in the absence of fermions; otherwise there is an effect of torsion on the dynamics of fields. We find that the conformal transformation of off-shell spin connection is not uniquely determined unless additional assumptions are made. One possibility gives rise to Nieh-Yan theory, another one to conformally invariant torsion; a one-parameter family of conformal transformations interpolates between the two. We also find that for dynamically generated torsion the spin connection does not have well defined conformal properties. In particular, it affects fermions and the non-minimally coupled conformal scalar field.

gr-qc↗

arXiv2019

Hamiltonian BRST formalism for gauge fields on black hole spacetimes

We investigate the Becchi-Rouet-Stora-Tyutin (BRST) formalism for gauge theories on spherically symmetric black hole spacetimes, with or without a cosmological constant ($Λ\geq0$). This is illustrated through the example of scalar electrodynamics. We first demonstrate that the horizons contribute additional surface terms to the Gauss law constraint of the theory when gauge transformations are not required to vanish on the horizons. We then consider the BRST invariant path integral including these surface terms following the Hamiltonian BRST formalism. We fix a radiation-like gauge which involves null components of the electromagnetic field at the horizons. We find that the presence of the surface terms in the constraint forces the ghost and gauge fixing actions to include additional surface integrals at the horizons. The null combination of the gauge fields at the horizons is shown to modify the ghost number charge of the theory through additional terms at the horizons. We also demonstrate how one can construct a gauge-fixing fermion which generates its own nilpotent symmetry transformations, called co-BRST transformations, that leave the theory invariant. The BRST and co-BRST transformations are further used to identify dressed (gauge invariant) fields of theory, whose dressings are affected by the presence of Killing horizons. We conclude with a discussion of potential applications of our results in soft limits and thermal field theories on black hole backgrounds.

gr-qc↗

arXiv2018

Constrained field theories on Kerr backgrounds

We analyze the constraints of gauge theories on Kerr and Kerr-de Sitter spacetimes, which contain one or more horizons. We find that the constraints are modified on such backgrounds through the presence of additional surface terms at the horizons. As a concrete example, we consider the Maxwell field and find that the Gauss law constraint involves surface corrections at the horizons. These surface contributions correspond to induced surface charges and currents on the horizons, which agree with those found within the membrane paradigm. The modification of the Gauss law constraint also influences the gauge fixing and Dirac brackets of the theory.

gr-qc↗

arXiv2018

Conformal scalar and torsion do not go together

We investigate the conformal transformation of vierbein-Einstein-Palatini (VEP) action in terms of tetrads $e^I_μ$ and spin connection $A^{IJ}_μ$. The transformation of the spin connection is indeterminate off-shell unless equations of motion are satisfied. We construct the conformally invariant scalar field in the torsion-free VEP formalism. In presence of fermionic matter, torsion does not vanish, and shows up in the dynamics of conformal scalar, affecting the invariance. It is not possible to maintain conformal invariance of the scalar field equation when fermions are present.

gr-qc↗

arXiv2017

Meissner effect and a stringlike interaction

We find that a recently proposed interaction involving the vorticity current of electrons, which radiatively induces a photon mass in 3+1 dimensions in the low-energy effective theory, corresponds to confining strings (linear potential) between electrons.

hep-th↗

arXiv2017

The inverse spatial Laplacian of spherically symmetric spacetimes

In this paper we derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson's equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de Sitter space in terms of hypergeometric functions.

gr-qc↗

arXiv2016

Constrained field theories on spherically symmetric spacetimes with horizons

We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.

gr-qc↗