Abstract
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) method, the second class constraints 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.
Highlights
The quantum mechanical analysis of the system in curved space has been examined about the ordering problem for a long time
For the first time we have explicitly constructed the BFFT Abelianization and BRST symmetry for the system of a non-relativistic particle constrained to a curved surface embedded in the higher dimensional Euclidean space in both Hamiltonian and Lagrangian formalism [50]
We have for the first time investigated BRST symmetry for a particle moving in a curved space VðN−1Þ embedded in a Euclidean space RN in both Hamiltonian and Lagrangian formalism
Summary
The quantum mechanical analysis of the system in curved space has been examined about the ordering problem for a long time. For the first time we have explicitly constructed the BFFT Abelianization and BRST symmetry for the system of a non-relativistic particle constrained to a curved surface embedded in the higher dimensional Euclidean space in both Hamiltonian and Lagrangian formalism [50]. To the best of our knowledge BRST formulation for a non-relativistic particle constrained to a curved surface embedded in the higher dimensional Euclidean space which is nonlinear constrained system and is a toy model for a wide class of physical systems has not been developed yet. This motivates us in the study of BRST symmetry for this system.
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