Nonperturbative Fermion Propagator, The Axial Ward Identity And Dynamical Electroweak Symmetry Breaking

In this thesis, we present a field-theoretical derivation of the nonperturbative fermion propagator in configuration space and construct its momentum space representation, which leads to the relevant Feynman rules. We also present an argument for the vanishing of such a propagator in Euclidean space via its contour integral representation.;We demonstrate that the nonperturbative fermion propagator contributions to the VVA and VVP triangle diagrams uphold the anomalous axial Ward identity to leading and next-to-leading order in the expansion parameter {dollar}m\sbsp{lcub}quark{rcub}{lcub}2{rcub}/p\sp2{dollar}, as well as in the expansion parameter {dollar}m\sbsp{lcub}\pi{rcub}{lcub}2{rcub}/m\sbsp{lcub}quark{rcub}{lcub}2{rcub}{dollar} appropriate for {dollar}\pi\sp0 \to \ \gamma\gamma{dollar} kinematics. We also utilize the Feynman-rule approach to verify the same identity in the absence of any explicit expansion.;We examine the contributions of the nonperturbative fermion propagator, associated with a weak-SU(2) doublet of condensing fermions, to the electroweak vacuum polarization functions. In the custodial SU(2) symmetry case of equal masses and condensates, we find that such contributions generate the standard electroweak symmetry breaking pattern, entirely decoupled from oblique radiative corrections. In the maximally asymmetric case, of which only the upper member of the doublet forms a condensate, we recover the same symmetry breaking pattern if the mass of the lower member is much smaller than that of the upper member. For this case, the upper member condensate contributions are shown to affect the oblique radiative corrections. The identification of this doublet with (t,b) is excluded by phenomenological considerations. If this doublet is identified with a subsequent fermion family, the present data rule out an upper-member mass less than 5{dollar}m\sb{lcub}Z{rcub}{dollar}