Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Particle on a Torus Knot: Constrained Dynamics and Semi-Classical
  Quantization in a Magnetic Field   Kinematics and dynamics of a particle moving on a torus knot poses an
interesting problem as a constrained system. In the first part of the paper we
have derived the modified symplectic structure or Dirac brackets of the above
model in Dirac's Hamiltonian framework, both in toroidal and Cartesian
coordinate systems. This algebra has been used to study the dynamics, in
particular small fluctuations in motion around a specific torus. The spatial
symmetries of the system have also been studied.
  In the second part of the paper we have considered the quantum theory of a
charge moving in a torus knot in the presence of a uniform magnetic field along
the axis of the torus in a semiclassical quantization framework. We exploit the
Einstein - Brillouin - Keller (EBK) scheme of quantization that is appropriate
for multidimensional systems. Embedding of the knot on a specific torus is
inherently two dimensional that gives rise to two quantization conditions. This
shows that although the system, after imposing the knot condition reduces to a
one dimensional system, even then it has manifest non-planar features which
shows up again in the study of fractional angular momentum. Finally we compare
the results obtained from EBK (multi-dimensional) and Bohr-Sommerfeld (single
dimensional) schemes. The energy levels and fractional spin depend on the torus
knot parameters that specifies its non-planar features. Interestingly, we show
that there can be non-planar corrections to the planar anyon-like fractional
spin.

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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs