Hamiltonian Effective Potentials.
Abstract
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 oneloop levels in the selfinteracting 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 1loop 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 NambuJonaLasinio 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 nexttoleading order gap equation are discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT.......188B
 Keywords:

 Physics: Elementary Particles and High Energy