Hamiltonian Effective Potentials.

Scalar and fermionic field theories in Schrodinger representation and methods of predicting mass generating phase transitions in this representation are discussed. A Hamiltonian effective potential is defined and calculated at tree and one-loop levels in the self-interacting phi^4 scalar field theory. The loop expansion for eigenfunctionals is equivalent to a combination of WKB expansion and expansion around constant field configurations. The potential at tree level coincides with the potential obtained from Lagrangian effective potential methods, while at 1-loop level, the potentials differ. Physical predictions from the two potentials agree, however. Bound state energies are directly calculated from the Schrodinger equation for excited states. The 2 + 1 dimension Nambu-Jona-Lasinio model for interacting fermions is investigated in Schrodinger representation in the large N_{f} limit, where N_{f} is the number of fermions. The leading order mass gap equation is derived and is found to coincide with the standard mass gap equation. Possible methods of obtaining the next-to-leading order gap equation are discussed.