Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of the $SU(N)$ $T$-algebra and the loop representation
  in $1+1$-dimensions   We consider the phase-space of Yang-Mills on a cylindrical space-time ($S^1
\times {\bf R}$) and the associated algebra of gauge-invariant functions, the
$T$-variables. We solve the Mandelstam identities both classically and
quantum-mechanically by considering the $T$-variables as functions of the
eigenvalues of the holonomy and their associated momenta. It is shown that
there are two inequivalent representations of the quantum $T$-algebra. Then we
compare this reduced phase space approach to Dirac quantization and find it to
give essentially equivalent results. We proceed to define a loop representation
in each of these two cases. One of these loop representations (for $N=2$) is
more or less equivalent to the usual loop representation.

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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-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
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: supr-con