  It is shown that the frequency of the de Haas van Alphen effect in
nonsuperconducting metals at very low temperatures is significantly corrected
by a perturbative term which appears in the Landau equation sequel to an
extension of the Pauli equation. The correction to the frequency of the de Haas
van Alphen oscillations is found to depend on the Fermi energy and the
measurable anomalous part of the electron gyro-magnetic factor. Furthermore, it
is shown that as a consequence of the perturbing term the electronic specific
heat Cv of a dilute, degenerate Fermi gas, under high magnetic field induction
greater that 25 Tesla and at ultra-low temperatures of the order of one milli
Kelvin shows an anomalous behavior, and at a finite temperature becomes
vanishingly small, i.e Cv is approximately zero, as the temperature approaches
absolute zero. Precision measurement at low temperatures and high magnetic
fields of the magneto optical absorption in simple band semiconductors is
suggested as an immediate way of detecting the modification of the Landau
levels due to the weak perturbation term which corrects in a magnetic field,
the kinetic energy of the electrons.
