Particle on a torus knot: symplectic analysis

Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold II

“…In the limit L ⟶ ðN − 1Þ, the system will return to system in [1]. The results developed in the manuscript have been verified using a model of particle on torus knot [82][83][84][85][86]. At the end, BV-BRST quantization of the BFFT Abelianized system will be investigated [87][88][89][90].…”

“…As an example of L-dimensional embedding in R N , we will discuss particle on torus knot [82][83][84][85][86]. We will discuss all the important results developed for general system in this case.…”

“…Thus, the matrix between the constraints will take exactly the same form of matrix Δ ab ij in Equation ( 26). As all the constraints of the theory (86) are second class, we will follow the method of Section 4 and introduce four possible fields Θ að1Þ , Θ að2Þ , Θ að3Þ , Θ að4Þ corresponding to each constraint. Relation between these fields will provide us possible value of ω abij .…”

Symplectic gauge-invariant reformulation of a free-particle system on toric geometry

“…The physicality condition satisfied by these charges shows that the first-class constraints annihilate the physical states of the system and it is on par with the Dirac quantization procedure [3]. For future endeavor, it will be an interesting venture to explore a particle moving on the torus knot within this framework and the results of the same shall be reported elsewhere soon [25]. * * *…”