Hamiltonian and Lagrangian BRST quantization in Riemann Manifold II

TL;DR

This paper extends the BRST quantization framework from hypersurfaces in Euclidean space to more general embedded manifolds, confirming the approach's consistency through a specific particle motion example.

Contribution

It generalizes the Hamiltonian and Lagrangian BRST quantization formalism to L-dimensional manifolds embedded in R^N, expanding its applicability.

Findings

Formalism successfully generalized to L-dimensional manifolds.

Results verified with a particle on a torus knot example.

Approach remains consistent with previous hypersurface case.

Abstract

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.