Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of a Unique Local Solution to the Many-body
  Maxwell-Schr\"odinger Initial Value Problem   We study the many-body problem of charged particles interacting with their
self-generated electromagnetic field. We model the dynamics of the particles by
the many-body Maxwell-Schr\"odinger system, where the particles are treated
quantum mechanically and the electromagnetic field is a classical quantity. We
prove the existence of a unique local in time solution to this nonlinear
initial value problem using a contraction mapping argument.

9
The categories of this paper are: nlin
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The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas