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Application of some algebraic arguments to the theory of normal Fermi systems
A. Ya. Povzner
Abstract:
A study is made of the many-particle operator
$$
H=\sum_1^N(-\Delta_k)+\sum_{i<j}V(|x_i-x_j|).
$$
Under the assumption that the system of Fermi particles in a volume
$\Omega$,
$N/\Omega=p$, it
is shown that there exists a formal operator series
$S$ such that
$HS\Psi_{\alpha}=SF\Psi_{\alpha}$, where
$F$ is a function of only the occupation number operators, and $\Psi_{\alpha}=a^*_{\alpha_1}\dots a^*_{\alpha_N}\Psi^0$,
where ,
$\Psi^0$ – is the vacuum vector. The series
$F$ is a series in powers of the density;
knowledge of
$F$ makes it possible to calculate the Gibbs potential at “low” densities but
in the whole temperature range. The relation to the Landau theory of normal Fermi
fluids is discussed. The first two terms of the series for
$F$ are calculated. A number
of questions relating to the passage to the limit
$\Omega\to\infty$ is discussed.
Received: 14.12.1971
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