arXiv subjects
Publications and source records attributed to Vipul Kumar Pandey.
In the present work we will give an explicit solution the problem of divergence of propagator of gauge-invariant Siegel-Zwiebach action in Fierz-Pauli gauge in massless limit by connecting its Greens functions to that of Transverse-Traceless gauge using improved finite-field-dependent BRST method.
We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical model amounts to a Dirac-Bergmann singular system, whose constraints restrict the actual dynamics to occur within a differential submanifold, as is the case in the major part of field theoretical models with gauge symmetry. We apply the Dirac-Bergmann algorithm in its full generality unraveling a total of $4m$ second-class constraints and obtain the corresponding Dirac brackets algebra in phase space. We follow with the Faddeev-Jackiw-Barcelos-Wotzasek approach in which the geometric character of the mentioned submanifold is emphasized by means of an internal metric function encoding its symplectic properties. We consider two straightforward examples, applying our general results to constrained motion along a toroidal geometry and to a Lorentz violating toy model in field theory. Since toroidal geometry has been recently used in cosmological models, we suggest how our results could lead to different proposals for the shape of the universe in cosmology.
We discuss the divergent graviton propagator massless limit problem in $D=26$ and show how it can be rigorously approached by interconnecting distinct gauge-fixed Siegel-Zwiebach generating functionals from string theory in the critical dimension through proper finite-field-dependent BRST (FFBRST) transformations. The massive Fierz-Pauli Lagrangian can be obtained from the gauge-invariant Siegel-Zwiebach one in the unitary gauge as a particular case, however suffering from the van Dam-Veltman-Zakharov discontinuity and possessing a ill-defined propagator in the massless limit. Nevertheless, alternatively working in a more suitable generalized Lorenz type gauge, including the transverse-traceless case, the graviton propagator for the Siegel-Zwiebach Lagrangian in the massless limit can be made finite. Gauge attainability and nilpotent BRST symmetries are explicitly worked out. We write down the complete corresponding generating functional, including the ghosts sector, and construct a convenient FFBRST transformation connecting the unitary gauge to a new bi-parametrized class of gauge-fixings containing the transverse traceless case. By taking into account the corresponding change in the Feynman integral Jacobian, a finite massless continuous limit propagator is achieved and fully justified.
We have previously developed the BRST quantization on the hypersurface $V_{N-1}$ embedded in N dimensional Euclidean space $R_N$ in both Hamiltonian and Lagrangian formulation. We generalize the formalism in the case of L dimensional manifold $V_L$ embedded in $R_N$ with $1\leq L < N$. The result is essentially the same as the previous one. We have also verified the results obtained here using a simple example of particle motion on a torus knot.
The BRST quantization of particle motion on the hypersurface $V_{(N-1)}$ embedded in Euclidean space $R_N$ is carried out both in Hamiltonian and Lagrangian formalism. Using Batalin-Fradkin-Fradkina-Tyutin (BFFT) formalism, the second class constrained obtained using Hamiltonian analysis are converted into first class constraints. Then using BFV analysis the BRST symmetry is constructed. We have given a simple example of these kind of system. In the end we have discussed Batalin-Vilkovisky formalism in the context of this (BFFT modified) system.
We perform the BFV-BRST quantization of the fourth-order Pais-Uhlenbeck oscillator (PUO). We show that although the PUO is not naturally constrained in the sense of Dirac-Bergmann, it is possible to profit from the introduction of suitable constraints in phase space in order to obtain a proper BRST invariant quantum system. Starting from its second-class constrained system description, we use the BFFT conversional approach to obtain first-class constraints as gauge symmetry generators. After the Abelianization of the constraints, we obtain the conserved BRST charge, the corresponding BRST transformations and proceed further to the BFV functional quantization of the model. We show that different possible gauge choices can be connected by finite field-dependent BRST transformations.
We apply the BFFT formalism to a prototypical second-class system, aiming to convert its constraints from second- to first-class. The proposed system admits a consistent initial set of second-class constraints and an open potential function providing room for applications to mechanical models as well as field theory such as the non-linear sigma model. The constraints can be arbitralily non-linear, broadly generalizing previously known cases. We obtain a sufficient condition for which a simple closed expression for the Abelian converted constraints and modified involutive Hamiltonian can be achieved. As explicit examples, we discuss a particle on a torus and a spontaneous Lorentz symmetry breaking vector model, obtaining in both situations the full first-class abelianized constraints in closed form and the corresponding involutive Hamiltonian.
We consider Polyakov theory of Bosonic strings in conformal gauge which are used to study conformal anomaly. However it exhibits ghost number anomaly. We show how this anomaly can be avoided by connecting this theory to that of in background covariant harmonic gauge which is known to be free from conformal and ghost number current anomaly, by using suitably constructed finite field dependent BRST transformation.
We show how Weyl degrees of freedom, can be introduced in the Nambu-Goto string in the path integral formulation using reparametrization invariant measure. We first identify Weyl degrees in conformal gauge using BFV formulation. Further we change Nambu-Goto string action to Polyakov action. The generating functional in light-cone gauge is then obtained from the generating func- tional corresponding to Polyakov action in conformal gauge by using suitably constructed finite field dependent BRST transformation.
We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.
We develop BRST symmetry for the first time for a particle on the surface of a torus knot by analyzing the constraints of the system. The theory contains $2^{nd}$ class constraints and has been extended by introducing Wess-Zumino term to the convert it into a theory with first class constraints. BFV analysis of the extended theory is performed to construct BRST/anti-BRST symmetries for the particle on torus knot. The nilpotent BRST/anti-BRST charges which generate such symmetries are constructed explicitly. The states annihilated by these nilpotent charges consist the physical Hilbert space. We indicate how various effective theories on the surface of the torus knot are related through the generalized version of BRST transformation with finite field dependent parameters.
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.