Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact sum rules for inhomogeneous systems containing a zero mode   We show that the formulas for the sum rules for the eigenvalues of
inhomogeneous systems that we have obtained in two recent papers are incomplete
when the system contains a zero mode. We prove that there are finite
contributions of the zero mode to the sum rules and we explicitly calculate the
expressions for the sum rules of order one and two. The previous results for
systems that do not contain a zero mode are unaffected.

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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: eess
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga