  Functional integral methods provide a way to define mean--field theories and
to systematically improve them. For the Hubbard model and similar
strong--correlation problems, methods based in particular on the
Hubbard--Stratonovich transformation have however been plagued by difficulties
to formulate the problem in a spin--rotation invariant way. Here a formalism
circumventing this problem by using a space-- and time--dependent spin
reference axis is discussed. This formulation is then used to suggest a
possible alternative to Nagaoka ferromagnetism in the strongly correlated
Hubbard model in the vicinity of half--filling. Finally, some aspects of
single--particle spectra in a simplified model for a short--range ordered
antiferromagnet are discussed.
