The magnetic properties of a two-dimensional interacting electron syst
em in a strong magnetic field are considered in the quantum Hall regim
e, where the motion of the electrons is restricted to the lowest Landa
u level. We apply an approach based on the many-particle quantum-field
theory which we developed recently for the spin-polarized system in t
he fractional quantum Hall regime, and which treats the problem of the
degeneracy of a partially filled Landau level properly. Via a gauge t
ransformation of the fermion Green's function, we achieve a dressing o
f the propagator with multiple collective excitations. Our theory allo
ws a calculation of the magnetic polarization M(T) for higher temperat
ures T, where M(T)less than or similar to 0.4 is not too large. For fi
lling factor nu=1 we obtain a magnetic polarization M(T) which agrees
quite well with the data of a NR?IR experiment by Barrett [Phys. Rev.
Lett. 74, 5112 (1995)].