Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On effects of gauging on symplectic structure, the Hopf term coupled to
  CP^1 model, and fractional spin   We couple the Hopf term to the relativistic $CP^1$ model and carry out the
Hamiltonian analysis at the classical level. The symplectic structure of the
model given by the set of Dirac Brackets among the phase space variables is
found to be the same as that of the pure $CP^1$ model. This symplectic
structure is shown to be inherited from the global SU(2) invariant $S^3$ model,
and undergoes no modification upon gauging the U(1) subgroup, except the
appearance of an additional first class constraint generating U(1) gauge
transformation. We then address the question of fractional spin as imparted by
the Hopf term at the classical level. For that we construct the expression of
angular momentum through both symmetric energy-momentum tensor as well as
through Noether's prescription. Both the expressions agree for the model
indicating no fractional spin is imparted by this term at the classical level-a
result which is at variance with what has been claimed in the literature. We
provide an argument to explain the discrepancy and corroborate our argument by
considering a radiation gauge fixed Hopf term coupled to $CP^1$ model, where
the desired fractional spin is reproduced and is given in terms of the soliton
number. Finally, by making the gauge field of the $CP^1$ model dynamical by
adding the Chern-Simons term, the model ceases to be a $CP^1$ model, as is the
case with its nonrelativistic counterpart. This model is also shown to reveals
the existence of `anomalous' spin. This is however given in terms of the total
charge of the system, rather than any soliton number.

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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cs