Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS
  Representations, the WKB Expansion, and Applications   This paper is part II of a series of papers on the deformation quantization
on the cotangent bundle of an arbitrary manifold $Q$. For certain homogeneous
star products of Weyl ordered type (which we have obtained from a Fedosov type
procedure in part I, see q-alg/9707030) we construct differential operator
representations via the formal GNS construction (see q-alg/9607019). The
positive linear functional is integration over $Q$ with respect to some fixed
density and is shown to yield a reasonable version of the Schr\"odinger
representation where a Weyl ordering prescription is incorporated. Furthermore
we discuss simple examples like free particle Hamiltonians (defined by a
Riemannian metric on $Q$) and the implementation of certain diffeomorphisms of
$Q$ to unitary transformations in the GNS (pre-)Hilbert space and of time
reversal maps (involutive anti-symplectic diffeomorphisms of $T^*Q$) to
anti-unitary transformations. We show that the fixed-point set of any
involutive time reversal map is either empty or a Lagrangean submanifold.
Moreover, we compare our approach to concepts using integral formulas of
generalized Moyal-Weyl type. Furthermore we show that the usual WKB expansion
with respect to a projectable Lagrangean submanifold can be formulated by a GNS
construction. Finally we prove that any homogeneous star product on any
cotangent bundle is strongly closed, i. e. the integral over $T^*Q$ w.r.t. the
symplectic volume vanishes on star-commutators. An alternative Fedosov type
deduction of the star product of standard ordered type using a deformation of
the algebra of symmetric contravariant tensor fields is given.

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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn