Particle on a torus knot: a Hamiltonian analysis

Abstract

We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The equations of motion are obtained for a path in general where the knot is present in the particle orbit but it is not restricted to a particular torus. We also study the motion when it is restricted to a specific torus. The rotational symmetries are studied as well. We have also considered the behavior of small fluctuations of the particle motion about a fixed torus knot.

Results are included in arXiv:1511.09035 (replaced); Particle on a Torus Knot: Constrained Dynamics and Semi-Classical Quantization in a Magnetic Field Praloy Das, Souvik Pramanik, Subir Ghosh