![]() The results developed in the manuscript have been verified using a model of particle on torus knot. In the limit, the system will return to system in. Then, the BRST charge and symmetries will be constructed for this BFFT Abelianized system using BFV method with the help of Faddeev-Senjanovic technique. The BFFT method will be used to convert the second class constraints to first class one. The system is shown to contain second-class constraints. We will do the constraint analysis of this system using the Dirac’s technique. This motivates us in the study of BRST symmetry for this system. To the best of our knowledge, there is no literature available which studied the BRST symmetry for a particle moving on a hypersurface embedded in the Euclidean space. BRST symmetry plays very significant role in renormalization of spontaneously broken gauge theories like standard model and hence is of very high significance for different kind of systems. In this quantization method, we enlarge the total Hilbert space of the gauge system under study and bring back the gauge symmetry of the gauge fixed action in the extended phase space, keeping the physical contents of the theory unchanged. It has also been found to be symmetry of general class of constrained systems. īecchi-Rout-Stora-Tyutin (BRST) quantization is on of the most significant technique to deal with a system with constraints. This has motivated us to extend our previous work to more general class of systems discussed in. These systems and the various properties they possess have been investigated by many authors. Here, a nonrelativistic particle constrained to move on a curved surface embedded in the higher dimensional Euclidean space has been taken. ![]() At the same time, the quantization of dynamical systems constrained to curved manifolds embedded in the higher-dimensional Euclidean space has been extensively investigated as one of the quantum theories. It is well known in the literature that the quantization of the system in curved space has been extensively studied about the ordering problem using two different approaches, canonical and path integral. This is the motivation of the present manuscript. ![]() In this sense, the considerations in the previous manuscript should be extended to general Riemannian manifolds. It is a well-known result in differential geometry that any -dimensional Riemann manifold can be locally embedded in the -dimensional Euclidean space but cannot be embedded in dimension generally. In the previous work we have considered the BRST quantization of the motion on a hypersurface embedded in the -dimensional Euclidean space based on Batalin-Fradkin-Fradkina-Tyutin (BFFT) Abelianized Batalin-Fradkin-Vilkovisky (BFV) and Batalin-Vilkovisky (BV) formalisms. We have also verified the results obtained here using a simple example of particle motion on a torus knot. The result is essentially the same as the previous one. We generalize the formalism in the case of -dimensional manifold embedded in with. We have previously developed the BRST quantization on the hypersurface embedded in -dimensional Euclidean space in both Hamiltonian and Lagrangian formulation.
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