Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Spectrum of the Neumann Matrix with Zero Modes   We calculate the spectrum of the matrix M' of Neumann coefficients of the
Witten vertex, expressed in the oscillator basis including the zero-mode a_0.
We find that in addition to the known continuous spectrum inside [-1/3,0) of
the matrix M without the zero-modes, there is also an additional eigenvalue
inside (0,1). For every eigenvalue, there is a pair of eigenvectors, a
twist-even and a twist-odd. We give analytically these eigenvectors as well as
the generating function for their components. Also, we have found an
interesting critical parameter b_0 = 8 ln 2 on which the forms of the
eigenvectors depend.

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The categories of this paper are: cs
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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: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: atom-ph