The energy \( E \) of a single particle is given by:
\[
E = \sqrt{p^2c^2 + m^2c^4}
\]
where \( p \) is the momentum, \( m \) is the mass of the fermions, and \( c \) is the speed of light. At zero temperature, all states up to the Fermi momentum \( p_F \) are
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