  We consider the Hartree equation for infinitely many electrons with a
constant external magnetic field. For the system, we show a local
well-posedness result when the initial data is the pertubation of a Fermi sea,
which is a non-trace class stationary solution to the system. In this case, the
one particle Hamiltonian is the Pauli operator, which possesses distinct
properties from the Laplace operator, for example, it has a discrete spectrum
and infinite-dimensional eigenspaces. The new ingredient is that we use the
Fourier-Wigner transform and the asymptotic properties of associated Laguerre
polynomials to derive a collapsing estimate, by which we establish the local
well-posedness result.
