The Standard Model of particle physics is analyzed for the case of a Higgs potential not favoring spontaneous electroweak symmetry breaking to gain insight into the physics of the Standard Model. Electroweak breaking still takes place, and quarks and leptons still acquire masses but through bosonic technicolor. This “other” phase of the Standard Model exhibits interesting phenomena.

The question of a phase transition in exiting the Planck epoch of the early universe is addressed. An order parameter is proposed to help decide the issue, and estimates are made concerning its behavior. Our analysis is suggestive that a phase transition occurred.

A theta term, which couples to topological charge, is added to the two-dimensional lattice CP3 model and U(1) gauge theory. Monte Carlo simulations are performed and compared to strong-coupling character expansions. In certain instances, a flattening behavior occurs in the free-energy at sufficiently large theta, but the effect is an artifact of the simulation methods.

Addressed is the question of whether a natural mechanism exists to resolve the strong CP problem. The analogous issue for the two-dimensional $CP^{N-1}$ models is analyzed using computer simulations.

A theta term, which couples to topological charge, is added to the lattice CPN-1 model. The strong-coupling character expansion is developed. The series for the free energy and mass gap are, respectively, computed to tenth order and fourth order. Several features of the strong-coupling analysis emerge. One is the loss of superconfinement. Another is that, in the intermediate coupling constant region, there are indications of a transition to a deconfining phase when theta is sufficiently large. The transition is like the one which has been observed in Monte Carlo simulations of a similar lattice CPN-1 action.

An approximate vacuum wave functional {Psi}{sub 0} is proposed for (2+1)-dimensional Yang-Mills theories. Using {Psi}{sub 0}, one can compute the 0{sup ++} glueball mass M{sub G} in terms of the string tension. By using the idea of dimensional reduction, a prediction for M{sub G} can be made in 3+1 dimensions. One finds M{sub G}{approx}1.5 GeV. {copyright} {ital 1997} {ital The American Physical Society}

An approximate vacuum wave functional Psi(0) is proposed for (2+1)-dimensional Yang-Mills theories. Using Psi(0), one can compute the 0(++) glueball mass M-G in terms of the string tension. By using the idea of dimensional reduction, a prediction for M-G can be made in 3+1 dimensions. One finds M-G approximate to 1.5 GeV.

Energy eigenstates for N = 2 supersymmetric gauged quantum mechanics are found for the gauges groups SU(n) and U(n). The analysis is aided by the existence of an infinite number of conserved operators. The spectum is continuous. Eigenstates at zero coupling for N > 2 are also presented, a case which is relevant for the conjectured description of M theory in the infinite momentum frame.

An approximation is used that permits one to explicitly solve the two-point Schwinger-Dyson equations of the U(N) lattice chiral models. The approximate solution correctly predicts a phase transition for dimensions d greater than two. For d less than or equal to 2, the system is in a single disordered phase with a mass gap. The method reproduces known N = infinity results well for d = 1. For d = 2, there is a moderate difference with N = infinity results only in the intermediate coupling constant legion.

A {theta} term, which couples to topological charge, is added to the two-dimensional lattice CP{sup 3} model and U(1) gauge theory. Monte Carlo simulations are performed and compared to strong-coupling character expansions. In certain instances, a flattening behavior occurs in the free energy at sufficiently large {theta}, but the effect is an artifact of the simulation methods. {copyright} {ital 1997} {ital The American Physical Society}

The annihilation of electron-positron pairs around one second after the big bang distorts the Fermi-Dirac spectrum of neutrino energies. We determine the distortions assuming neutrino mixing with an inverted neutrino-mass hierarchy. Nonequilibrium thermodynamics, the Boltzmann equation, and numerical integration are used to achieve the results. The various types of neutrino behavior are established as a function of masses and mixing angles.

Four-dimensional twisted group lattices are used as models for space-time structure. Compared to other attempts at space-time deformation they have two main advantages: They have a physical interpretation and there is no difficulty in putting field theories on these structures. We present and discuss ordinary and gauge theories on twisted group lattices. We solve the free field theory case by finding all the irreducible representations. The non-abelian gauge theory on the two-dimensional twisted group lattice is also solved. On twisted group lattices, continuous space-time translational and rotational symmetries are replaced by discrete counterparts. We discuss these symmetries in detail. Four-dimensional twisted group lattices can also be used as models for non-trivial discrete compactifications of certain ten-dimensional spaces.

We present analytical solutions to the nonlinear equations describing the behavior of a gas of neutrinos with two flavors. Self-maintained coherent flavor oscillations are shown to occur when the gas density exceeds a critical value determined by the neutrino masses and the mean neutrino energy in the gas. Similar oscillations may have occurred in the early Universe.

The antibracket formalism for gauge theories, at both the classical and quantum level, is reviewed. Gauge transformations and the associated gauge structure are analyzed in detail. The basic concepts involved in the antibracket formalism are elucidated. Gauge-fixing, quantum effects, and anomalies within the field-antifield formalism are developed. The concepts, issues and constructions are illustrated using eight gauge-theory models.

We consider oscillations of neutrinos under conditions in which the neutrino density is sufficiently large that neutrino-neutrino interactions cannot be neglected. A formalism is developed to treat this highly nonlinear system. Numerical analysis reveals a rich array of phenomena. In certain gases, a self-induced Mikheyev-Smirnov-Wolfenstein effect occurs in which electron neutrinos are resonantly converted into muon neutrinos. In another relatively low-density gas, an unexpected parametric resonant conversion takes place. Finally, neutrino-neutrino interactions maintain coherence in one system for which a priori one expected decoherence.

The high-temperature expansion for the partition function of the Ising model on the truncated icosahedron lattice is computed exactly. The average energy and heat capacity are presented.

Nuclear simulations of neutrino oscillations in the early Universe are performed for a neutrino-mass hierarchy with the vacuum mass of the second neutrino exceeding that of the first. This situation is equivalent to a normal hierarchy with mixing angle greater than π4. We find that a large conversion of electron neutrinos to muon neutrinos occurs, independent of mixing angle. For certain parameter values, this is caused by the MSW effect. In the rest of the parameter region a new mechanism is operative, arising from nonlinear effects involving neutrino-neutrino forward scattering. This nonlinear conversion mechanism causes substantial flavor oscillation even for extremely small mixing angles.

Numerical studies are performed for neutrino oscillations for t > 1/3 seconds after the big bang. The effects of electron, positron and neutrino backgrounds are properly included. Flavor evolution of the neutrino background is dominantly smooth. However, in a certain parameter region, coherent undamped oscillations of the neutrino background are possible. In addition, neutrino CP asymmetry is found to be considerably smaller than expected. Reasons are provided for the above effects and some physical implications are discussed.

We determine the electronic energy levels of C60 using a combination of theoretical and experimental results. The hopping Hamiltonian for the truncated icosahedron is solved analytically for the unequal coupling case using group lattice methods. Then, an analysis of previously preformed experiments on electronic structure is undertaken. When these approaches are combined, a fairly clear picture of the location of the electronic levels emerges.