We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest the trick of replacing the initial Hamiltonian by a Dirac Hamiltonian. This allows us to do easily a perturbation theory and derive a supermatrix $\sigma$ model, which takes a form of the conventional $\sigma$ model with the unitary symmetry. Using this $\sigma$ model we calculate several correlation functions including a spin-spin correlation function. As compared to the model without spin, we get different expressions for the single-particle lifetime and the transport time. The diffusion constant turns out to be 2 times smaller than the one for spinless particles.

• Received 8 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.165304