  We quantize a particle confined to move on a torus knot satisfying constraint
condition ($p \theta + q \phi) \approx 0$, within the context of a
geometrically motivated approach - the Faddeev-Jackiw formalism. We also deduce
the constraint spectrum and discern the basic brackets of the theory. We
further reformulate the original gauge non-invariant theory into a physically
equivalent gauge theory, which is free from any additional Wess-Zumino
variables, by employing symplectic gauge invariant formalism. In addition, we
analyze the reformulated gauge invariant theory within the framework of BRST
formalism to establish the off-shell nilpotent and absolutely anti-commuting
(anti-)BRST symmetries. Finally, we construct the conserved (anti-)BRST charges
which satisfy the physicality criteria and turn out to be the generators of
corresponding symmetries.
