Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Vacuum Polarization Density Caused by an External Field   We consider an external potential, $-\lambda \phi$, due to one or more
nuclei. Following the Dirac picture such a potential polarizes the vacuum. The
polarization density as derived in physics literature, after a well known
renormalization procedure, depends decisively on the strength of $\lambda$. For
small $\lambda$, more precisely as long as the lowest eigenvalue,
$e_1(\lambda)$, of the corresponding Dirac operator stays in the gap of the
essential spectrum, the integral over the density vanishes. In other words the
vacuum stays neutral. But as soon as $e_1(\lambda)$ dives into the lower
continuum the vacuum gets spontaneously charged with charge $ 2e$. Global
charge conservation implies that two positrons were emitted out of the vacuum,
this is, a large enough external potential can produce electron-positron pairs.
  We give a rigorous proof of that phenomenon.

17
The categories of this paper are: q-fin
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph