Bhabani Prasad Mandal

A PT-invariant potential with complex QES eigenvalues

Abstract We show that the quasi-exactly solvable eigenvalues of the Schrodinger equation for the PT-invariant potential V ( x )=−( ζ cosh2 x − 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.

APPLICATION OF FINITE FIELD-DEPENDENT BRS TRANSFORMATIONS TO PROBLEMS OF THE COULOMB GAUGE

We discuss the Coulomb propagator in the formalism developed recently in which we construct the Coulomb gauge path-integral by correlating it with the well-defined Lorentz gauge path-integrals through a finite field-dependent BRS transformation. We discover several features of the Coulomb gauge from it. We find that the singular Coulomb gauge has to be treated as the gauge parameter λ → 0 limit. We further find that the propagator so obtained has good high energy behavior for λ ≠ 0 and ∊ ≠ 0. We also find that the behavior of the propagator so obtained is sensitive to the order of limits k0 → ∞, λ → 0 and ∊ → 0; so that these have to be handled carefully in a higher loop calculation. We show that we can arrive at the result of Cheng and Tsai for the ambiguous two-loop Feynman integrals without the need for an extra ad hoc regularization and within the path integral formulation.

Off-shell nilpotent finite Becchi–Rouet–Stora–Tyutin (BRST)/anti-BRST transformations

We develop the off-shell nilpotent finite field dependent BRST transformations and show that for different choices of the finite field dependent parameter these connect the generating functionals corresponding to different effective theories. We also construct both on-shell and off-shell finite field dependent anti-BRST tranformations for Yang Mills theories and show that these transformations play the similar role in connecting different generating functionals of different effective theories. Analogous to the finite field dependent BRST transformations, the non-trivial Jacobians of the path integral measure which arise due to the finite field dependent anti-BRST transformations are responsible for the new results. We consider several explicit examples in each case to demonstrate the results.

Finite BRST transformations for the Bagger–Lambert–Gustavsson theory

Abstract In this Letter we analyse the Bagger–Lambert–Gustavsson (BLG) theory in N = 1 superspace. Furthermore, we will construct the BRST transformations for this theory. These BRST transformations will be integrated out to obtain the finite field dependent version of BRST (FFBRST) transformations. We will also analyse the effect of the FFBRST transformations on the effective action. We will thus show that the FFBRST transformations can be used to relate generating functionals of the BLG theory in two different gauges.

Finite nilpotent symmetry in Batalin-Vilkovisky formalism

We consider the Batalin-Vilkovisky formulation of both 1-form and 2-form gauge theories in the context of generalized BRST transformations with a finite field-dependent parameter. In the usual Faddeev-Popov (FP) formulation of gauge theories such finite field-dependent BRST (FFBRST) transformations do not leave the generating functionals invariant as the path integral measure changes in a non-trivial way for finite transformations. Here we show that FFBRST transformation, with the appropriate choice of a finite field-dependent parameter, is the symmetry of the generating functionals in the Batalin-Vilkovisky formalism. The finite parameter is chosen in such a way that the contribution from the Jacobian of the path integral measure is adjusted with gauge fixed fermions which do not change the generating functionals. Several examples for such finite parameters are constructed.

Relating Gribov-Zwanziger theory to effective Yang-Mills theory

We consider the Gribov-Zwanziger (GZ) theory with appropriate horizon term which exhibits the nilpotent BRST invariance. This infinitesimal BRST transformation has been generalized by allowing the parameter to be finite and field dependent (FFBRST). By constructing appropriate finite field-dependent parameter we show that the generating functional of GZ theory with horizon term is related to that of Yang-Mills (YM) theory through FFBRST transformation.

GENERALIZED BRST TRANSFORMATION IN ABELIAN RANK-2 ANTISYMMETRIC TENSOR FIELD THEORY

We generalize the BRST transformations in Abelian rank-2 tensor field theory by allowing the parameter to be finite and field-dependent and show that such transformations play crucial role in studying the Abelian 2-form gauge theory in noncovariant gauges. The generating functionals in different effective theories are connected through these generalized BRST transformations with different choice of finite parameter. We further consider the generalization of the anti-BRST transformations and show that even anti-BRST transformations with the finite field dependent parameter relate the generating functional for different effective theories. Such generalized BRST/anti-BRST transformations are useful in connecting generating functionals corresponding to different effective theories. Field/antifield formulation of this Abelian 2-form gauge theory is also studied in the context of generalized BRST transformations. We show that generalized BRST transformation connects the generating functional corresponding to the different solutions of quantum master equation in field/antifield formulation.

Field dependent nilpotent symmetry for gauge theories

We construct the field dependent mixed BRST (combination of BRST and anti-BRST) transformations for pure gauge theories. These are shown to be an exact nilpotent symmetry of the effective action as well as the generating functional for certain choices of the field dependent parameters. We show that the Jacobian contributions for path integral measure in the definition of generating functional arising from BRST and anti-BRST part compensate each other. The field dependent mixed BRST transformations are also considered in the field/antifield formulation to show that the solutions of quantum master equation remain invariant under these. Our results are supported by several explicit examples.

Delayed pulsar kicks from the emission of sterile neutrinos

The observed velocities of pulsars suggest the possibility that sterile neutrinos with mass of several keV are emitted from a cooling neutron star. The same sterile neutrinos could constitute all or part of cosmological dark matter. The neutrino-driven kicks can exhibit delays depending on the mass and the mixing angle, which can be compared with the pulsar data. We discuss the allowed ranges of sterile neutrino parameters, consistent with the latest cosmological and x-ray bounds, which can explain the pulsar kicks for different delay times.

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.