BRST Symmetries in Free Particle System on Toric Geometry

Abstract

We study a free particle system residing on a torus to investigate its Becci-Rouet-Stora-Tyutin symmetries associated with its Stückelberg coordinates, ghosts and anti-ghosts. By exploiting zeibein frame on the toric geometry, we evaluate energy spectrum of the system to describe the particle dynamics. We also investigate symplectic structures involved in the second-class system on the torus.

BRST Symmetry and de Rham Cohomology

“…In this chapter, we show that this spectrum obtained by the Dirac method can be consistent with that of the improved Dirac Hamiltonian formalism at the level of the first class constraint by fixing ambiguity, and then we discuss its physical consequences [48]. We next study a free particle system residing on torus to investigate its first class Hamiltonian associated with its Stückelberg coordinates [56].…”

“…Now, we construct the first class Hamiltonian by introducing the Stückelberg coordinates associated with the geometrical constraints on torus [97]. To do this, we consider a free particle system residing on the torus, whose Lagrangian is of the form…”

“…We next investigate BRST symmetries of the free particle system residing on the torus. By exploiting zeibein frame on the toric geometry, we evaluate energy spectrum of the system to describe the particle dynamics [56].…”

“…Now, we find the BRST invariant gauge fixed Lagrangian and the corresponding BRST transformation rules of a free particle system on torus [97]. We also construct its spectrum.…”

“…On the other hand, the first class Hamiltonian was constructed by introducing Stückelberg coordinates associated with geometrical constraints on a torus, to yield BRST-invariant gauge fixed Lagrangian including ghosts and anti-ghosts and the corresponding BRST transformation rules [97]. The spectrum and the symplectic structures of the free particle was investigated on the torus [97].…”