Double Hodge Theory for a Particle on Torus

Abstract

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.

Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold

“…The nilpotent BRST charge is constructed in the operator form using the mode expansion of the fields [79,80]. The result has been verified using simple example of particle on torus [81][82][83][84]. At the end we will construct BRST transformation of the system using Batalin-Vilkovisky (BV) quantization method [86][87][88][89].…”

“…Particle on Torus. Particle on torus [81][82][83][84][85] is a two dimensional surface embedded in three dimensional space. It has been studied as a toy model for different type of field theories.…”

Symplectic gauge-invariant reformulation of a free-particle system on toric geometry

“…Consequently, we have shown that the first-order Lagrangian constructed via the symplectic gauge-invariant formalism is invariant under the transformations generated by the set of first-class constraints. One of the striking features of our work is that the reformulated gauge-invariant theory is free from Wess-Zumino variables unlike [20,21,23].…”

“…Whereas in the domain of quantum field theories, a free-particle system on toric geometry has been explored within the Batalin-Fradkin-Vilkovisky framework [20]. Moreover, for the same system, the off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries have been established within the framework of superfield formalism [21,22] and it has been shown to behave as a model for the double Hodge theory [23].…”

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

“…Our goal is to obtain and exhibit the converted Abelian first-class constraints and modified involutive Hamiltonian in closed form for this particular example to clarify the ideas introduced in the last two sections. The particle on a torus has been recently discussed in reference [57] through the finite field dependent BRST formalism [58,59,60], exploring the BRST symmetry generators algebra. Other aspects of this model, concerning its canonical quantization, energy spectrum, superfield approach and BRST symmetries, can be seen in [61,62,63].…”