Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $CP^{1}$ model with Hopf interaction: the quantum theory   The $CP^1$ model with Hopf interaction is quantised following the
Batalin-Tyutin (BT) prescription. In this scheme, extra BT fields are
introduced which allow for the existence of only commuting first-class
constraints. Explicit expression for the quantum correction to the expectation
value of the energy density and angular momentum in the physical sector of this
model is derived. The result shows, in the particular operator ordering that we
have chosen to work with, that the quantum effect has a divergent contribution
of $ {\cal O} (\hbar^2)$ in the energy expectation value. But, interestingly
the Hopf term, though topological in nature, can have a finite ${\cal O}
(\hbar)$ contribution to energy density in the homotopically nontrivial
topological sector. The angular momentum operator, however, is found to have no
quantum correction, indicating the absence of any fractional spin even at this
quantum level. Finally, the extended Lagrangian incorporating the BT auxiliary
fields is computed in the conventional framework of BRST formalism exploiting
Faddeev-Popov technique of path integral method.

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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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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: cond-mat