Fermions in Lattice Gauge Theory.

Spin 3/2 and 5/2 fields on the lattice are investigated. Species doubling is found to be curable with an analogue of Wilson's method and partially curable with an analogue of the Kogut -Susskind formalism. Only the latter preserves local supersymmetry but describes at least four species. SO(N) and SU(N) gauge theories with euclidean Susskind fermions giving two Dirac flavors in the continuum limit are investigated. Flavor aspects are elucidated at weak coupling and mass terms are constructed which break the flavor symmetry. At strong coupling the self interaction of massless baryons is found to cause dynamical symmetry breaking for (lamda) = 1/g('2)N with (lamda)(SU(N)) = 4.3/N, (lamda)(SO(N)) = 8.6/N. The effect of suppressing closed fermion loops (the quenched approximation) is investigated in some 1 + 1 dimensional field theories. In the Schwinger model and in the Thirring model it is found that effects of fermion loops on bound state masses can be absorbed in a rescaling of the coupling constant. In the Schwinger model an extra (decoupled) massless ghost appears and the order parameter <(')(psi)(psi)> becomes infrared divergent. In a strongly coupled U(1) lattice gauge theory with euclidean Susskind fermions the order parameter v = <(')(psi)(psi)> is computed with and without closed quark loops. The effect of the fermion determinant on v is found to be strongly suppressed by powers of 1/d. In four dimensions with massless quarks we find (DELTA)v/v = .78% at leadind order in 1/d for d = 4.