Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalization of Scattering States, Scattering Phase Shifts and
  Levinson's Theorem   We show that the normalization integral for the Schr\"odinger and Dirac
scattering wave functions contains, besides the usual delta-function, a term
proportional to the derivative of the phase shift. This term is of zero measure
with respect to the integration over momentum variables and can be discarded in
most cases. Yet it carries the full information on phase shifts and can be used
for computation and manipulation of quantities which depend on phase shifts. In
this paper we prove Levinson's theorem in a most general way which assumes only
the completeness of states. In the case of a Dirac particle we obtain a new
result valid for positive and negative energies separately. We also make a
generalization of known results, for the phase shifts in the asymptotic limit
of high energies, to the case of singular potentials. As an application we
consider certain equations, which arise in a generalized interaction picture of
quantum electrodynamics. Using the above mentioned results for the phase shifts
we prove that any solution of these equations, which has a finite number of
bound states, has a total charge zero. Furthermore, we show that in these
equations the coupling constant is not a free parameter, but rather should be
treated as an eigenvalue and hence must have a definite numerical value.

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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: acc-phys