arXiv subjects

Bhabani Prasad Mandal

Publications and source records attributed to Bhabani Prasad Mandal.

At least 91 records · Page 5Linked to original sources

arXiv2016

Scattering amplitudes for the rationally extended P T symmetric complex potentials

In this paper, we consider the rational extensions of two different P T symmetric complex potentials namely the asymptotically vanishing Scarf II and asymptotically non-vanishing Rosen-Morse II [ RM-II] potentials and obtain bound state eigenfunc- tions in terms of newly found exceptional Xm Jacobi polynomials and also some new type of orthogonal polynomials respectively. By considering the asymptotic behaviour of the exceptional polynomials, we obtain the reflection and transmission amplitudes for them and discuss the various novel properties of the corresponding amplitudes.

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arXiv2016

IR finite graviton propagators in de Sitter spacetime

Graviton propagator diverges in certain gauges in de Sitter spacetime. We address this problem in this work by generalizing the infinitesimal BRST transformations in de Sitter spacetime to finite field-dependent BRST (FFBRST) transformations. These FFBRST transformations are symmetry of the classical action, but do not leave path integral measure invariant for the graviton theory in de Sitter spacetime. Due to the non-trivial Jacobian of such finite transformation the path integral measure changes and hence FFBRST transformation is capable of relating theories in two different gauges. We explicitly construct FFBRST transformation which relates theory with diverging graviton two-point function to theory with infrared (IR) finite graviton. The FFBRST transformation thus establishes that divergence in graviton two-point function may be only a gauge artifact.

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arXiv2016

Maximal Abelian gauge and a generalized BRST transformation

We apply a generalized Becchi-Rouet-Stora-Tyutin (BRST) formulation to establish a connection between the gauge-fixed $SU(2)$ Yang-Mills (YM) theories formulated in the Lorenz gauge and in the Maximal Abelian (MA) gauge. It is shown that the generating functional corresponding to the Faddeev-Popov (FP) effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST) transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.

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arXiv2016

Imaginary Interactions with Minimum Length

We analyze the effect of having minimum length on a two dimensional anisotropic simple harmonic oscillator with PT symmetric imaginary interaction perturbatively. First order correction to the general state is calculated analytically to show that it remains real as long as PT symmetry is unbroken. The characteristics of PT phase transition remain unaltered in this deformed formulation of quantum mechanics.

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arXiv2015

Parametric symmetries in exactly solvable real and P T symmetric complex potentials

In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex P T symmetric potentials. We focus our at- tention on the conventional potentials such as the generalized Poschl Teller (GPT), o Scarf-I and P T symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials are shown to yield a completely dif- ferent behavior of the bound state solutions. Further the supersymmetric (SUSY) partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and P T symmetric complex potentials. These potentials are also observed to be shape invariant (SI) in nature. We subse- quently take up a study of the newly discovered rationally extended SI Potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs). We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2,1) algebra.

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arXiv2015

PT phase transition in a (2+1)-d relativistic system

We study a massless Dirac particle with PT symmetric non-Hermitian Rashba interaction in the background of Dirac oscillator potential to show the PT phase transition in a (2+1) dimensional relativistic system analytically. PT phase transition occurs when strength of the (i) imaginary Rashba interaction or (ii) transverse magnetic field exceed their respective critical values. Small mass gap in the spectrum, consistent with other approaches is generated as long as the system is in the unbroken phase. Relativistic Landau levels are constructed explicitly for such a system.

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arXiv2015

Emergence of Lowenstein-Zimmermann mass terms for QED$_{3}$

In this paper we consider a super-renormalizable theory of massless QED in $(2+1)$ dimensions and discuss their BRST symmetry transformation. By extending the BRST transformation we derive the Nielsen identities for the theory. Further, we compute the generalized BRST (so-called FFBRST) transformation by making the transformation parameter field-dependent. Remarkably, we observe that the Lowenstein-Zimmerman mass terms, containing Lowenstein-Zimmerman parameter which plays an important role in the BPHZL renormalization program, along with the external sources coupled to the non-linear BRST variations appear naturally in the theory through a FFBRST transformation.

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arXiv2015

Hartman-Fletcher effect for array of complex barriers

We calculate the time taken by a wave packet to tunnel through a series of complex barrier potentials using stationary phase method to show its saturation (Hartman-Fletcher effect) with number of barriers in various situations. We numerically study the effect of the coupling between the elastic and inelastic channels, width of the individual barrier, separation between the consecutive barriers on the saturation of tunneling time. Nature of HF effect has further been investigated for more realistic barriers with random inelasticity and also for emissive inelastic channels.

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arXiv2015

Green's Functions in Perturbative Quantum Gravity

We show that the Green's functions in non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation is also holds for operator Green's functions. We further derive the explicit relation between the Green's functions in the theory of perturbative quantum gravity in a pair of arbitary gauges. This process involves some sort of modified FFBRST transformations which is derivable from infinitesimal field-dependent BRST transformations.

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arXiv2015

Generalized BRST symmetry for arbitrary spin conformal field theory

We develop the finite field-dependent BRST (FFBRST) transformation for arbitrary spin-s conformal field theories. We discuss the novel features of the FFBRST transformation in these systems. To illustrate the results we consider the spin-1 and spin-2 conformal field theories in two examples. Within the formalism we found that FFBRST transformation connects the generating functionals of spin-1 and spin-2 conformal field theories in linear and non-linear gauges. Further, the conformal field theories in the framework of FFBRST transformation are also analysed in Batalin-Vilkovisky (BV) formulation to establish the results.

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arXiv2015

Equivalence between two different field-dependent BRST formulations

Finite field-dependent BRST (FFBRST) transformations were constructed by integrating infinitesimal BRST transformation in a closed form. Such a generalized transformations have been extended in various branch of physics and found many applications. Recently BRST transformation has also been generalized with same goal and motivation in slightly different manner. In this work we have shown that the later formulation is conceptually equivalent to the earlier formulation. We justify our claim by producing the same result of later formulation using earlier FFBRST formulation.

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arXiv2015

Group theoretic approach to rationally extended shape invariant potentials

The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new operator $U (x, J_3 \pm 1/2 )$ to express the Hamiltonian corresponding to these extended potentials in terms of Casimir operators. Connection between the potential algebra and the shape invariance is elucidated.

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arXiv2014

A superspace description of Chern-Simons theory in Batalin-Vilkovisky formulation

We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for the Chern-Simons (CS) theories in $(2+1)$ spacetime dimensions. Further we develop the superspace description of BV formulation for such theories. Interestingly, the extended BRST invariant CS theories can be described in superspace in covariant manner with the help of one more (Grassmann) coordinate. However, a superspace with two Grassmann coordinates are required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant actions for these theories.

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arXiv2014

Rationally extended shape invariant potentials in arbitrary D-dimensions associated with exceptional $X_m$ polynomials

Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in terms of X_m Laguerre or X_m Jacobi exceptional orthogonal polynomials. These potentials are isospectral to their usual counterparts and possess translationally shape invariance property.

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arXiv2014

A black potential for spin less particles

We consider the most general non-Hermitian Hulthen potential to study the scattering of spin-less relativistic particles. The conditions for CC, SS and CPA are obtained analytically for this potential. We show that almost total absorption occurs for entire range of incidence energy for certain parameter ranges of the potential and hence term this as `black potential'. Time reversed of the same potential shows perfect emission for the entire range of particle energy. We also present the classical analog of this potential in terms of waveguide cross section.

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arXiv2014

Reciprocity in parity violating non-Hermitian systems

Reciprocity is shown so far only when the scattering potential is either real or parity symmetric complex. We extend this result for parity violating complex potential by considering several explicit examples: (i) we show reciprocity for a PT symmetric (hence parity violating) complex potential which admits penetrating state solutions analytically for all possible values of incidence energy and (ii) reciprocity is shown to hold at certain discrete energies for two other parity violating complex potentials.

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arXiv2014

Finite field-dependent BRST symmetry for ABJM theory in ${\cal N}=1$ superspace

In this paper we analyse the ABJM theory in ${\cal N}=1$ superspace. Firstly we study the linear and non-linear BRST transformations for the ABJM theory. Then we derive the finite field dependent version of these BRST (FFBRST) transformations. Further we show that such FFBRST transformations relate the generating functional in linear gauge to the generating functional in the non-linear gauge of ABJM theory.

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arXiv2014

Complex Classical Mechanics of a QES Potential

We consider a Parity-time (PT) invariant non-Hermitian quasi-exactly solvable (QES) potential which exhibits PT phase transition. We numerically study this potential in a complex plane classically to demonstrate different quantum effects. The particle with real energy makes closed orbits around one of the periodic wells of the complex potential depending on the initial condition. However interestingly the particle can have open orbits even with real energy if it is initially placed in certain region between the two wells on the same side of the imaginary axis. On the other hand when the particle energy is complex the trajectory is open and the particle tunnels back and forth between two wells which are separated by a classically forbidden path. The tunneling time is calculated for different pair of wells and is shown to vary inversely with the imaginary component of energy. At the classical level unlike the analogous quantum situation we do not see any qualitative differences in the features of the particle dynamics for PT symmetry broken and unbroken phases.

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