Analysis on infinite-dimensional manifolds-Schroedinger representation for quantized fields

An approach to quantum field theory that is similar technique in quantum mechanics, called field theoretic Schroedinger representation is presented, introducing bosonic theories for describing how gauge theories appear within the Schroedinger representation. It is shown that the functional method allows exhibiting unambiguously non-trivial features, like extensions in the algebra of infinitesimal transformations and cocycles in the finite transformations. Various variational approximation, that are suggested for field theory by their quantum mechanical antecedents. This is done for static and time-dependent problems, for pure and mixed states. The subject of quantum fields in and out of thermal equilibrium is developed. It is shown how a Schroedinger representation can be given for Fermi models, which do not commute at equal times.(M.C.K.)