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Avinash Khare

Publications and source records attributed to Avinash Khare.

196 records · Page 11Linked to original sources
arXiv1995

Spontaneous Symmetry Breaking and the Renormalization of the Chern-Simons Term

We calculate the one-loop perturbative correction to the coefficient of the \cs term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual $U(1)$ symmetry, radiative corrections do not change the coefficient of the \cs term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant \cs term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the \cs term is a discontinuous function over the phase diagram of the theory.

hep-th↗
arXiv1995

Negaton and Positon Solutions of the KDV Equation

We give a systematic classification and a detailed discussion of the structure, motion and scattering of the recently discovered negaton and positon solutions of the Korteweg-de Vries equation. There are two distinct types of negaton solutions which we label $[S^{n}]$ and $[C^{n}]$, where $(n+1)$ is the order of the Wronskian used in the derivation. For negatons, the number of singularities and zeros is finite and they show very interesting time dependence. The general motion is in the positive $x$ direction, except for certain negatons which exhibit one oscillation around the origin. In contrast, there is just one type of positon solution, which we label $[\tilde C^n]$. For positons, one gets a finite number of singularities for $n$ odd, but an infinite number for even values of $n$. The general motion of positons is in the negative $x$ direction with periodic oscillations. Negatons and positons retain their identities in a scattering process and their phase shifts are discussed. We obtain a simple explanation of all phase shifts by generalizing the notions of ``mass" and ``center of mass" to singular solutions. Finally, it is shown that negaton and positon solutions of the KdV equation can be used to obtain corresponding new solutions of the modified KdV equation.

hep-th↗
arXiv1995

Chern-Simons Term and Charged Vortices in Abelian and Nonabelian Gauge Theories

In this article we review some of the recent advances regarding the charged vortex solutions in abelian and nonabelian gauge theories with Chern-Simons (CS) term in two space dimensions. Since these nontrivial results are essentially because of the CS term, hence, we first discuss in some detail the various properties of the CS term in two space dimensions. In particular, it is pointed out that this parity (P) and time reversal (T) violating but gauge invariant term when added to the Maxwell Lagrangian gives a massive gauge quanta and yet the theory is still gauge invariant. Further, the vacuum of such a theory shows the magneto-electric effect. Besides, we show that the CS term can also be generated by spontaneous symmetry breaking as well as by radiative corrections. A detailed discussion about Coleman-Hill theorem is also given which aserts that the parity-odd piece of the vacuum polarization tensor at zero momentum transfer is unaffected by two and multi-loop effects. Topological quantization of the coefficient of the CS term in nonabelian gauge theories is also elaborated in some detail. One of the dramatic effect of the CS term is that the vortices of the abelian (as well as nonabelian) Higgs model now acquire finite quantized charge and angular momentum. The various properties of these vortices are discussed at length with special emphasis on some of the recent developments including the discovery of the self-dual charged vortex solutions.

hep-th↗
arXiv1995

Truncated Harmonic Osillator and Parasupersymmetric Quantum Mechanics

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary order p can also be rewritten in terms of p supercharges (i.e. all of which obey $Q_i^{2} = 0$). However, the Hamiltonian cannot be expressed in a simple form in terms of the p supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, the p supercharges, the p conformal supercharges along with Hamiltonian H, conformal generator K and dilatation generator D form a closed algebra.

hep-th↗
arXiv1994

On the Coleman-Hill Theorem

The Coleman-Hill theorem prohibits the appearance of radiative corrections to the topological mass (more precisely, to the parity-odd part of the vacuum polarization tensor at zero momentum) in a wide class of abelian gauge theories in 2+1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum polarization tensor. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Simons electrodynamics, obeys the new non-renormalization theorem. Whereas the vacuum polarization {\sl does} receive a one-loop, parity-odd correction, this does not translate to a radiative contribution to the Chern-Simons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooked in the original analysis, where the conditions of the theorem are satisfied and where the topological mass does, in fact, get a radiative correction.

hep-th↗
arXiv1994

$B \wedge F$ Term by Spontaneous Symmetry Breaking in a generalized Abelian Higgs Model

We show that the topological $B \wedge F$ term in $3+1$ dimensions can be generated via spontaneous symmetry breaking in a generalized Abelian Higgs model. Further, we also show that even in $D$ dimensions $ ( D \geq 3 ) $, a $B \wedge F$ term gives rise to the topological massive excitations of the Abelian gauge field and that such a $B \wedge F$ term can also be generated via Higgs mechanism.

hep-th↗
arXiv1994

The Phase of the Riemann Zeta Function and the Inverted Harmonic Oscillator

The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. This leads to the analogy with the scattering amplitude, and an approximate rule for the location of the zeros. The smooth phase of the Zeta function along the line of the zeros is related to the quantum density of states of an inverted oscillator.

chao-dyn↗
arXiv1994

Supersymmetry and Quantum Mechanics

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large $N$ expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order $p$.

hep-th↗
arXiv1994

Self-Dual Charged Vortices of Finite Energy per Unit Length in $3+1$ Dimensions

We obtain both topological as well as nontopological self-dual charged vortex solutions of finite energy per unit length in a generalized abelian Higgs model in $3+1$ dimensions. In this model the Bogomol'nyi bound on the energy per unit length is obtained as a linear combination of the magnetic flux and the electric charge per unit length.

hep-th↗
arXiv1993

Comment on 'Anyon in External Elecromagnetic Field: Hamiltonian and Lagrangian Formulation'

We point out that in a recent paper by Chaichian et al. (Phys. Rev.Lett71(1993)3405) Dirac quantization procedure is not properly followed as a result of which the resulting quantum theory is different from what one will get by a straightforward application of Dirac's formulation. For example at quantum level the model in I has noncommutative geometry, i.e., $[x_μ, x_ν] \neq 0$ while a correct treatment would give $[x_μ, x_ν] = 0$. Moreover, their assertion about $α$ being an arbitrary constant in $S_μ= -αp_μ/{\sqrt{p^2}} $ is not correct and consequently one can not say whether the model describes anyons.

hep-th↗
arXiv1993

An improved calculation of the Third Virial Coefficient of a free anyon Gas

For three anyons confined in a harmonic oscillator, only the class of states that interpolate nonlinearly with the statistical parameter contributes to the third virial coefficient of a free anyon gas. Rather than evaluating the full three-body partition function as was done in an earlier publication (Phys. Rev. {\bf A46}, 4693 (1992)), here only the nonlinear contribution is calculated, thus avoiding delicate cancellations between the irrelevant linear part and the two-body partition function. Our numerical results are consistent with the simple analytical form suggested recently by Myrheim and Olaussen.

hep-th↗
arXiv1993

Some Exactly Solvable Three-Body Problems in One dimension

The three-body problem in one-dimension with a repulsive inverse square potential between every pair was solved by Calogero. Here, the known results of supersymmetric quantum mechanics are used to propose a number of new three-body potentials which can be solved algebraically. Analytic expressions for the eigenspectrum and the eigenfunctions are given with and without confinement.

hep-th↗
arXiv1993

Supersymmetry,Shape Invariance and Exactly Solvable Noncentral Potentials

Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends the list of exactly solvable potentials for which the solution can be obtained algebraically in a simple and elegant manner. As an illustration, we discuss in detail the example of the potential $$V(r,θ,ϕ)={ω^2\over 4}r^2 + {δ\over r^2}+{C\over r^2 sin^2θ}+{D\over r^2 cos^2θ} + {F\over r^2 sin^2θsin^2 αϕ} +{G\over r^2 sin^2θcos^2αϕ}$$ with 7 parameters.Other algebraically solvable examples are also given.

hep-th↗
arXiv1993

One parameter family of Compacton Solutions in a class of Generalized Korteweg-DeVries Equations

We study the generalized Korteweg-DeVries equations derivable from the Lagrangian: $ L(l,p) = \int \left( \frac{1}{2} φ_{x} φ_{t} - { {(φ_{x})^{l}} \over {l(l-1)}} + α(φ_{x})^{p} (φ_{xx})^{2} \right) dx, $ where the usual fields $u(x,t)$ of the generalized KdV equation are defined by $u(x,t) = φ_{x}(x,t)$. For $p$ an arbitrary continuous parameter $0< p \leq 2 ,l=p+2$ we find compacton solutions to these equations which have the feature that their width is independent of the amplitude. This generalizes previous results which considered $p=1,2$. For the exact compactons we find a relation between the energy, mass and velocity of the solitons. We show that this relationship can also be obtained using a variational method based on the principle of least action.

patt-sol↗
arXiv1993

New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.

hep-ph↗