Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ghost story. III. Back to ghost number zero   After having defined a 3-strings midpoint-inserted vertex for the bc system,
we analyze the relation between gh=0 states (wedge states) and gh=3 midpoint
duals. We find explicit and regular relations connecting the two objects. In
the case of wedge states this allows us to write down a spectral decomposition
for the gh=0 Neumann matrices, despite the fact that they are not commuting
with the matrix representation of K1. We thus trace back the origin of this
noncommutativity to be a consequence of the imaginary poles of the wedge
eigenvalues in the complex k-plane. With explicit reconstruction formulas at
hand for both gh=0 and gh=3, we can finally show how the midpoint vertex avoids
this intrinsic noncommutativity at gh=0, making everything as simple as the
zero momentum matter sector.

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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: physics