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We construct a charged vectorial field in the global limit of a U(1) chiral lattice gauge theory and, using the hopping parameter expansion, calculate its propagator. We show that the doubler modes are removed and that it is possible to tune a bare Yukawa-like coupling to obtain a finite mass for this field in the continuum limit. Related results are given for the propagators of chiral fermions.

We study the decoupling of doubler modes and the requisite tuning of the lattice fermion mass {ital am}{sub {ital f}}=0 (necessary for a finite {ital m}{sub {ital f}}/{ital m}{sub bosonic} in the continuum limit) for a formulation of the SU(2){times}U(1){sub {ital Y}} electroweak theory on the lattice.

Using a hopping parameter expansion, we demonstrate the decoupling of fermion doubler modes in the hypercharge U(1)Y lattice gauge theory. We also show analytically that it is possible to tune the bare Yukawa coupling to a value such that the fundamental physical fermion amf=0 (as is necessary in order to obtain a finite physical mass mf in the continuum limit), and we calculate this value. The appropriate special case of these results is compared with numerical simulations of the frozen-gauge limit of the U(1)Y theory, and good agreement is found. The role of the Yukawa coupling in a chiral lattice gauge theory is contrasted with that in a nonchiral Yukawa model.

It is conjectured that the lack of chiral gauge symmetry-preserving regulator is signalling a genuine quantum effect which breaks chiral gauge symmetries and generates masses for gauge bosons. This idea is applied to an SU(3) C ×SU(2) L ×U(1) Y model. It is shown that the dynamics of chiral fermions can generate masses for the W and Z bosons with the correct mass ratio. Chiral gauge theories without elementary scalars are found to be related to effective gauge theories with group element valued scalar fields. Furhtermore, massless fermions can exist in such theories.

We study the (zero-temperature) chiral transition in an SU(2) lattice gauge theory with I = 1 2 Higgs fields, and fermion fields with I = 1 2 and I = 0 , including Yukawa couplings. Using analytic methods in the strong gauge coupling limit, we demonstrate that (i) if at least one of the Yukawa couplings is sufficiently weak, this theory undergoes a spontaneous chiral symmetry breaking phase transition; (ii) this transition is removed when the Yukawa couplings are sufficiently strong. The transition is determined to be of second order, and approximate critical point calculations are given. Some implications for the continuum limit of the SU(2) model, and for electroweak interactions, are discussed.

We study the chiral phase structure for SU(2) lattice gauge theory with an I = 12 Higgs field and I = 1 dynamical fermions. The order and location of the chiral transition for strong gauge coupling are in agreement with our previous analytic results. In the interior of the phase diagram, it is found that the chiral boundary lies above the line of transitions connecting to the O(4) critical point. This study elucidates the effect of fermion representation on the chiral transition and strengthens the basis for a possible explanation for the fact that the known weak nonsinglet fermions have I = 12.

We suggest a possible explanation, based on properties of the (zero-temperature) chiral transition in lattice gauge-Higgs theories, for why the known left-handed fermions have weak isospin 1 2 .

The phase diagram of lattice SU(2) gauge theory with fundamental representation Higgs fields is probed by l= 1 2 and l =1 fermions. Quenched calculations of 〈 Ψ Ψ〉 l show two distinct regions characterized by broken or unbroken chiral symmetry. The location of the boundary between the two regions depends on the representation l of the fermions. For l= 1 2 fermions the presence is verified of Nambu-Goldstone bosons (“pions”) in the broken region and evidence is found for massless physical fermions in the chirally symmetric region. Effects of boundary conditions and the possibility of observing two particle cuts in finite lattice spectrum calculations are commented on also.

We consider the possibility that the lack of a chiral gauge symmetry-preserving regulator is signaling a genuine quantum effect which breaks the chiral gauge symmetry and generates mass for the gauge bosons. A nonperturbative analysis of an SU(3)C×SU(2)L×U(1)Y model regularized on a lattice is presented. Although both SU(2)L and U(1) Y symmetries in this model are broken in the regularized action, SU(3)C×U(1)Q symmetry can be maintained throughout the calculations. Using a hopping parameter expansion, the effective action for the gauge bosons is derived. Mass terms for the gauge bosons are generated, and the mass ratio of the gauge bosons is discussed.

We present an analytic study of the (zero-temperature) chiral symmetry-breaking phase transition in SU(2) lattice gauge-Higgs theory with fermions, relevant to the SU(2) sector of the standard electroweak theory. The transition is found to be second-order and the critical gauge-Higgs coupling is calculated in the limit of strong gauge coupling. New Monte Carlo measurements for quenched I = 1 2 fermions are presented and found to be in excellent agreement with the analytic results, which are not limited to the quenched approximation.

We report new results in three areas concerning the chiral transition in U(1) lattice gauge-Higgs theory with fermions. First, the case of a theory with two differently charged fermions simultaneously present is studied, and it is shown analytically that there are two associated continuous chiral phase transitions. Second, a general theorem is proved classifying the strong gauge-coupling behavior of any U(1) theory with a fermion and Higgs fields of arbitrary nonzero charges q f and q h : such a theory has a chiral transitions along the β g = 0 line if and only if q f is a nonzero multiple of q h . Third, new data is presented on the chiral transition with quenched fermions in the interiof of the phase diagram at small or zero gauge-Higgs coupling, completing our earlier mapping of the chiral phase boundary.

We report the first measurements, with fully dynamical fermions, of the (zero-temperature) chiral symmetry-breaking phase transition in the SU (2) part of the standard SU(2)×U(1) electroweak lattice gauge theory. These are performed with a Langevin algorithm. Good agreement is found with the previous analytic strong gauge coupling results, regarding both the location and the order of the transition. The chiral boundary is also measured in the interior of the phase diagram and the phase structure with dynamical fermions is discussed.