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Bhabani Prasad Mandal

Publications and source records attributed to Bhabani Prasad Mandal.

140 records · Page 8Linked to original sources
arXiv2003

Exciton in Matrix Formulation of Quantum Hall Effect

The quantum Hall effect is studied by introducing two different matrix variables for electrons and holes, having Chern-Simons type interactions. By generalizing the constraint condition proposed by Susskind to realize the Pauli's exclusion principle in this two component matrix model, the classical exciton solution having excitation of both quasi-electron and quasi-hole is obtained. The constraint condition is also solved quantum mechanically in the infinite-sized matrix case, giving the examples of the physical states. Using these quantum states, the corrections of the exciton energy, coming from the noncommutativity of space (Pauli principle) and from the quantum effects of the background state, are estimated in the lowest order perturbation expansion. As a result, the dispersion relation of exciton is obtained.

hep-th↗
arXiv2001

On an exactly solvable $B_N$ type Calogero model with nonhermitian PT invariant interaction

An exactly solvable many-particle quantum system is proposed by adding some nonhermitian but PT invariant interactions to the $B_N$ Calogero model. We have shown that such extended $B_N$ Calogero model leads to completely real spectrum which obey generalised exclusion statistics. It is also found that the corresponding exchange statistics parameter exhibit `reflection symmetry' provided the strength of a PT invariant interaction exceeds a critical value.

cond-mat.stat-mech↗
arXiv2000

Quantum gauge symmetry from finite field dependent BRST transformations

Using the technique of finite field dependent BRST transformations we show that the classical massive Yang-Mills theory and the pure Yang-Mills theory whose gauge symmetry is broken by a gauge fixing term are identical from the view point of quantum gauge symmetry. The explicit infinitesimal transformations which leave the massive Yang-Mills theory BRST invariant are given.

hep-th↗
arXiv2000

PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

We show that at least the quasi-exactly solvable eigenvalues of the Schrödinger equation with the potential $V(x) = -(ζ\cosh 2x -iM)^2$ as well as the periodic potential $V(x) = (ζ\cos 2θ-iM)^2$ are real for the PT-invariant non-Hermitian potentials in case the parameter $M$ is any odd integer. We further show that the norm as well as the weight functions for the corresponding weak orthogonal polynomials are also real.

quant-ph↗
arXiv2000

A PT-Invariant Potential With Complex QES Eigenvalues

We show that the quasi-exactly solvable eigenvalues of the Schrödinger equation for the PT-invariant potential $V(x) = -(ζ\cosh 2x -iM)^2$ are complex conjugate pairs in case the parameter M is an even integer while they are real in case M is an odd integer. We also show that whereas the PT symmetry is spontaneously broken in the former case, it is unbroken in the latter case.

quant-ph↗
arXiv1999

Path Integral Solution to Non-central Potential

We have studied the path integral solution of a system of particle moving in certain class of non-central potential without using Kustannheimo-Stiefel transformation. The Hamiltonian of the system has been converted to a separable Hamiltonian of Liouville type in parabolic coordinates and has further reduced to a Hamiltonian corresponding to two 2- dimensional simple harmonic oscillators. The energy spectrum for this system is calculated analytically. Hartmann ring-shaped potential and compound Coulomb plus Aharanov- Bohm potential have also been studied as special cases.

quant-ph↗
arXiv1999

A superspace formulation of Abelian antisymmetric tensor gauge theory

We apply a superspace formulation to the four-dimensional gauge theory of a massless Abelian antisymmetric tensor field of rank 2. The theory is formulated in a six-dimensional superspace using rank-2 tensor, vector and scalar superfields and their associated supersources. It is shown that BRS transformation rules of fields are realized as Euler-Lagrange equations without assuming the so-called horizontality condition and that a generating functional $\bar{W}$ constracted in the superspace reduces to that for the ordinary gauge theory of Abelian rank-2 antisymmetric tensor field. The WT identity for this theory is derived by making use of the superspace formulation and is expressed in a neat and compact form $\partial\bar{W}/\partialθ=0$.

hep-th↗
arXiv1999

A superspace formulation of an "asymptotic" OSp(3,1|2) invariance of Yang-Mills theories

We formulate a superspace field theory which is shown to be equivalent to the $c-\bar{c}$ symmetric BRS/Anti-BRS invariant Yang-Mills action. The theory uses a 6-dimensional superspace and one OSp(3,1|2) vector multiplet of unconstrained superfields. We establish a superspace WT identity and show that the formulation has an asymptotic OSp(3,1|2) invariance as the gauge parameter goes to infinity. We give a physical interpretation of this asymptotic OSp(3,1|2) invariance as a symmetry transformation among the longitudinal/time like degrees of freedom of $A_μ$ and the ghost degrees of freedom.

hep-th↗
arXiv1998

A Number of Quasi-Exactly Solvable N-body Problems

We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form an orthogonal set and many of their properties are similar to those of the Bender-Dunne polynomials. We also discuss QES problems where the polynomials do not form an orthogonal set.

quant-ph↗
arXiv1997

Anti-isospectral Transformations, Orthogonal Polynomials and Quasi-Exactly Solvable Problems

We consider the double sinh-Gordon potential which is a quasi-exactly solvable problem and show that in this case one has two sets of Bender-Dunne orthogonal polynomials . We study in some detail the various properties of these polynomials and the corresponding quotient polynomials. In particular, we show that the weight functions for these polynomials are not always positive. We also study the orthogonal polynomials of the double sine-Gordon potential which is related to the double sinh-Gordon case by an anti-isospectral transformation. Finally we discover a new quasi-exactly solvable problem by making use of the anti-isospectral transformation.

quant-ph↗
arXiv1997

Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?

We consider two quasi-exactly solvable problems in one dimension for which the Schrödinger equation can be converted to Heun's equation. We show that in neither case the Bender-Dunne polynomials form an orthogonal set. Using the anti-isopectral transformation we also discover a new quasi-exactly solvable problem and show that even in this case the polynomials do not form an orthogonal set.

math-ph↗
arXiv1997

D-brane interaction in the type IIB Matrix Model

We calculate the potential between bound states of D-branes of different dimension in IIB matrix model upto one loop order and find nice agreement with the open string calculations in short and large distance limit. We also consider the scattering of bound states of D-branes, calculate the scattering phase shift and analyze the effective potential in different limits.

hep-th↗
arXiv1995

Local BRS Transformations and Osp(3,1|2) Symmetry of Yang-Mills Theories

We consider a certain local generalization of BRS transformations of Yang-Mills theory in which the anti-commuting parameter is space time dependent. While these are not exact symmetries, they do lead to a new nontrivial WT identity. We make a precise connection between the ``local BRS "and the broken orthosymplectic symmetry recently found in superspace formulation of Yang-Mills theory by showing that the local BRS WT identity is precisely the WT identity obtained in the superspace formulation via a superrotation. This ``local BRS " WT identity could lead to new consequences not contained in the usual BRS WT identity.

hep-th↗