Lanczos’s quaternionic interpretation of Dirac’s equation provides a unified description for all elementary particles of spin 0, 1 2 , 1, and 3 2 . The Lagrangian formulation given by Einstein and Mayer in 1933 predicts two main classes of solutions. (1) Point like partons which come in two families, quarks and leptons. The correct fractional or integral electric and baryonic charges, and zero ...

There is relatively intense interest at present in exploring more deeply and widely the suggestion' that the mathematical methods essential to the understanding of material media which exhibit long-range order (ferromagnets, superconductors, etc. ) may also be basic or useful for the theory of elementary particles. The original work had two connected aspects: the generation of fermion masses (b...

These lectures focus on the structure of various Higgs boson theories. Topics in the first lectures include: mass generation in chiral theories, spontaneous symmetry breaking, neutrino masses, perturbative unitarity, vacuum stability, vacuum alignment, flavor changing neutral current solutions with multiple Higgs doublets, analysis of type I theory with Z2 symmetry, and rephasing symmetries. Af...

In supersymmetric theories, the Peccei-Quinn symmetry has a complex extension as a symmetry of the superpotential, so that the scalar potential always has an almost flat direction, the dilaton. We discuss how coherent oscillation of the dilaton affects axion cosmology. We stress that the dilaton decay, if its dominant mode is not into axions, releases large entropy at a late epoch of the Univer...

We develop a theory of electric-field-induced magnetization of a medium. The relevant polarizability, βCP , simultaneously violates the inversion symmetry (parity), the time-reversal symmetry, and the combined CP symmetry. We focus on two fundamental mechanisms mediating the appearance of βCP — the electric dipole moment of the electron (eEDM) and the electron-nucleus pseudo-scalar weak neutral...

We present a series of hypotheses and speculations leading inescapably to the conclusion that SU(5) is the gauge group of the world~hat all elementary particle forces (strong, weak, and electromagnetic) are different manifestations of the same fundamental interaction involving a single coupling strength, the fine-structure constant. Our hypotheses may be wrong and our speculations idle, but the...

We calculate the region of the MSSM parameter space (i.e. M1/2, m0, μ, . . . ) compatible with a correct electroweak breaking and a realistic top-quark mass. To do so we have included all the one-loop corrections to the effective potential V1 and checked their importance in order to obtain consistent results. We also consider the fine-tuning problem due to the enormous dependence of MZ on ht (t...

Effective chiral Lagrangians involving constituent quarks, Goldstone bosons and long-distance gluons are believed to describe the strong interactions in an intermediate energy region between the confinement scale and the chiral symmetry breaking scale. Baryons and mesons in such a description are bound states of constituent quarks. We discuss the combined use of the techniques of effective chir...

We use the theory of crystal graphs to give a simple graph-theoretical algorithm for determining the branching rule for decomposing a representation of a simple Lie algebra when restricted to a simple subalgebra. We also describe a computer package for determining such decomposi-tions graphically. 0.1 Introduction When modeling elementary particle interactions and symmetry breaking in physics i...