Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical expansions up to $\hbar^4$-order in relativistic nuclear
  physics   We present the first calculation of the $\hbar^4$-Wigner--Kirkwood
corrections to a relativistic system of fermions in the presence of external
scalar and vector potentials. The method we propose allows to compute
efficiently semiclassical corrections to one body operators such as mean
energies and local densities. It also preserves gauge invariance and produces
explicitly convergent results despite some apparent divergencies at the
classical turning points. As a byproduct we obtain the $\hbar^4$ corrections
stemming from the polarization of the Dirac sea. We apply our results to the
relativistic $\sigma$-$\omega$ Lagrangian in the Hartree valence approximation.
We compare the semiclassical expansion with the exact result and with the
Strutinsky average whenever it can be obtained. We find that the $\hbar^4 $
corrections are much smaller than typical shell effects. Our results provide
convincing arguments to neglect higher than second order $\hbar$ effects in the
Wigner--Kirkwood scheme to relativistic nuclear physics in the mean field
approximation.

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The categories of this paper are: acc-phys
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: math
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn