arXiv subjects

Amitabha Lahiri

Publications and source records attributed to Amitabha Lahiri.

At least 73 records · Page 4Linked to original sources

arXiv2011

Particle with non-Abelian charge: classical and quantum

We study the action for a non-Abelian charged particle in a non-Abelian background field in the worldline formalism, described by real bosonic variables, leading to the well known equations given by Wong. The isospin parts in the action can be viewed as the Lagrange multiplier term corresponding to a non-holonomic constraint restricting the isospins to be parallel transported. The path integration is performed over the isospin variables and as a result, the worldlines turn out to be constrained by the classical solutions for the isospins. We derive a wave equation from the path integral, constructed as the constrained Hamiltonian operator acting on the wave function. The operator ordering corresponding to the quantum Hamiltonian is found and verified by the inverse Weyl transformation.

hep-th↗

arXiv2011

No hair theorems for stationary axisymmetric black holes

We present a non-perturbative proof of the no hair theorems corresponding to scalar and Proca fields for stationary axisymmetric de Sitter black hole spacetimes. Our method also applies to asymptotically flat and under a reasonable assumption, to asymptotically anti-de Sitter spacetimes.

gr-qc↗

arXiv2010

Path space forms and surface holonomy

We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of higher gauge theory, where end points of the path need not be fixed.

math-ph↗

arXiv2010

Parallel Transport over Path Spaces

We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework.

math-ph↗

arXiv2010

On the existence of cosmological event horizon

We show that, for general static or axisymmetric stationary spacetimes, a cosmological Killing horizon exists only if $R_{ab}n^{a}n^{b}< 0$ for a hypersurface orthogonal timelike $n^{a}$, at least over some portion of the region of interest of the manifold. This implies violation of the strong energy condition by the matter fields, the simplest example of which is a positive cosmological constant.

gr-qc↗

arXiv2010

Cosmic strings with positive $Λ$

We discuss cosmic Nielsen-Olesen strings in space-times endowed with a positive cosmological constant. For the cylindrically symmetric, static free cosmic string, we discuss the contribution of the cosmological constant to the angle deficit, and to the motion of the null/timelike geodesics. For a non-gravitating cosmic string in a Schwarzschild-de Sitter space-time, we discuss how a thin string can pierce the two horizons. We also present a metric which describes the exterior of a self gravitating thin string present in the Schwarzschild-de Sitter space-time.

gr-qc↗

arXiv2009

Flux dualization in broken SU(2)

An SU(2) gauge theory is broken to U(1) by an adjoint scalar to produce magnetic monopoles. At a lower scale, this U(1) is further broken by a fundamental scalar to produce tubes of magnetic flux. We dualize the resulting theory to write an effective theory in terms of the macroscopic string variables. The monopoles are attached to the ends of the strings, and the flux is confined in the tubes.

hep-th↗

arXiv2009

Monopoles and flux strings from SU(2) adjoint scalars

We construct, in an SU(2) gauge theory with two adjoint scalars, flux strings with monopoles attached at the ends. One scalar breaks SU(2) to U(1) and produces monopoles, the other then breaks the U(1) and produces strings. Dualizing, we write the theory in terms of effective string variables and show that the flux in the string is exactly saturated by the monopoles at the ends.

hep-th↗

arXiv2008

Effect of a positive cosmological constant on cosmic strings

We study cosmic Nielsen-Olesen strings in space-times with a positive cosmological constant. For the free cosmic string in a cylindrically symmetric space-time, we calculate the contribution of the cosmological constant to the angle deficit, and to the bending of null geodesics. For a cosmic string in a Schwarzschild-de Sitter space-time, we use Kruskal patches around the inner and outer horizons to show that a thin string can pierce them.

gr-qc↗

arXiv2007

Negative forms and path space forms

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.

math-ph↗

arXiv2007

No hair theorems for positive Λ

We extend all known black hole no-hair theorems to space-times endowed with a positive cosmological constant $Λ.$ Specifically, we prove that static spherical black holes with $Λ>0$ cannot support scalar fields in convex potentials and Proca-massive vector fields in the region between black hole and cosmic horizons. We also demonstrate the existence of at least one type of quantum hair, and of exactly one charged solution for the Abelian Higgs model. Our method of proof can be applied to investigate other types of quantum or topological hair on black holes in the presence of a positive $Λ.$

gr-qc↗

arXiv2007

Confinement of monopole using flux string

We study the confinement of fermionic magnetic monopoles by a thin flux tube of the Abelian Higgs model. Parity demands that the monopole currents be axial. This implies that the model is consistent only if there are at least two species of fermions being confined.

hep-ph↗

arXiv2007

Generalized vector field

We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.

math-ph↗

arXiv2006

Generalized forms and vector fields

The generalized vector is defined on an $n$ dimensional manifold. Interior product, Lie derivative acting on generalized $p$-forms, $-1\le p\le n$ are introduced. Generalized commutator of two generalized vectors are defined. Adding a correction term to Cartan's formula the generalized Lie derivative's action on a generalized vector field is defined. We explore various identities of the generalized Lie derivative with respect to generalized vector fields, and discuss an application.

math-ph↗

arXiv2006

Monopole confinement by flux tube

We revisit Nambu's model of quark confinement by a tube of magnetic flux, with two additional features. The quarks are taken to be magnetic monopoles external to the tube, which seal the ends, and are also taken to be fermions. This ensures that the model is inconsistent unless there are at least two species of fermions being confined.

hep-ph↗

arXiv2004

Parallel transport on non-Abelian flux tubes

I propose a way of unambiguously parallel transporting fields on non-Abelian flux tubes, or strings, by means of two gauge fields. One gauge field transports along the tube, while the other transports normal to the tube. Ambiguity is removed by imposing an integrability condition on the pair of fields. The construction leads to a gauge theory of mathematical objects known as Lie 2-groups, which are known to result also from the parallel transport of the flux tubes themselves. The integrability condition is also shown to be equivalent to the assumption that parallel transport along nearby string configurations are equal up to arbitrary gauge transformations. Attempts to implement this condition in a field theory leads to effective actions for two-form fields.

hep-th↗

arXiv2004

Surface holonomy and gauge 2-group

Just as point objects are parallel transported along curves, giving holonomies, string-like objects are parallel transported along surfaces, giving surface holonomies. Composition of these surfaces correspond to products in a category theoretic generalization of the gauge group, called a 2-group. I consider two different ways of constructing surface holonomies, one by using a pair of one and two form connections, and another by using a pair of one-form connections. Both procedures result in the structure of a 2-group.

hep-th↗

arXiv2001

Local symmetries of the non-Abelian two-form

It is proposed that a non-Abelian adjoint two-form in BF type theories transform inhomogeneously under the gauge group. The resulting restrictions on invariant actions are discussed. The auxiliary one-form which is required for maintaining vector gauge symmetry transforms like a second gauge field, and hence cannot be fully absorbed in the two-form. But it can be replaced, via a vector gauge transformation, by the usual gauge field, leading to gauge equivalences between different types of theories. A new type of symmetry also appears, one which depends on local functions but cannot be generated by constraints. It is connected to the identity in the limit of a vanishing global parameter, so it should be called a semiglobal symmetry. The corresponding conserved currents and BRST charges are parametrized by the space of flat connections.

hep-th↗