Abstract
In this chapter, we first proceed to investigate symplectic structure involved in the free particle system on the torus [56]. We next investigate nonholonomic constrained system with second class constraints, using Hamilton-Jacobi quantization scheme to yield complete equations of motion of the system [104].
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Notes
- 1.
As before, the super-Poisson bracket is defined as \(\{A,B\} = \frac{\delta A} {\delta q} \vert _{r}\frac{\delta B} {\delta p} \vert _{l} - (-1)^{\eta _{A}\eta _{B}}\frac{\delta B} {\delta q} \vert _{r}\frac{\delta A} {\delta p} \vert _{l}\) where η A denotes the number of fermions, called the ghost number, in A and the subscript r and l denote right and left derivatives, respectively.
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Hong, ST. (2015). Symplectic Embedding and Hamilton-Jacobi Quantization. In: BRST Symmetry and de Rham Cohomology. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9750-4_4
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