Spontaneous Symmetry Breaking and Chiral Symmetry

In this introductory lecture, some basic features of the spontaneous symmetry breaking are discussed. More specifically, $\sigma$-model, non-linear realization, and some examples of spontaneous symmetry breaking in the non-relativistic system are discussed in details. The approach here is more pedagogical than rigorous and the purpose is to get some simple explanation of some useful topics in this rather wide area. .Comment: Lecture Delivered at VII Mexico Workshop on Paritcles and Fields, Merida, Yucatan Mexico, Nov 10-17,199

On Vector Goldstone Boson

The possibility that higher dimensional field theories are broken spontaneously, through the usual Nambu-Goldstone mechanism, to 4-dimension is explored. As a consequence, vector Goldstone bosons can arise in this breaking of Lorentzian symmetry from higher dimension to 4-dimension. This can provide a simple mechanism for reduction to 4-dimension in theories with extra dimensions.Comment: 6 pages, equations, submitted for publicatio

Consistency of Loop Regularization Method and Divergence Structure of QFTs Beyond One-Loop Order

We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the general procedure. In the processes, we find a new divergence structure: the regulated result for each two-loop diagram contains a gauge-violating quadratic harmful divergent term even combined with their corresponding counterterm insertion diagrams. Only when we sum up over all the relevant diagrams do these quadratic harmful divergences cancel, recovering the gauge invariance and locality.Comment: 33 pages, 5 figures, Sub-section IIIE removed, to be published in EPJ

Matrix elements of four-quark operators and \Delta L=2 hyperon decays

The study of neutrinoless double beta decays of nuclei and hyperons require the calculation of hadronic matrix elements of local four-quark operators that change the total charge by two units \Delta Q=2 . Using a low energy effective Lagrangian that induces these transitions, we compute these hadronic matrix elements in the framework of the MIT bag model. As an illustrative example we evaluate the amplitude and transition rate of \Sigma- -> p e- e-, a decay process that violates lepton number by two units (\Delta L=2). The relevant matrix element is evaluated without assuming the usual factorization approximation of the four-quark operators and the results obtained in both approaches are compared.Comment: 13 pages, 2 .eps figure

Spin and Flavor Contents of the Proton

After a brief review of the experimental results obtained in deep inelastic lepton-nucleon scatterings and the Drell-Yan processes and their implications for the spin and flavor contents of the nucleon, we suggest that those features, that are contrary to the expectations of the naive quark model, can all be accounted for in the chiral quark model of Georgi and Manohar. In our formulation of the chiral quark model, the $\eta ^{\prime }$ meson is seen to play an important role.Comment: Corrected a latex error and added report #'s in the revised version. Latex and Revtex, 7 pages, Invited talk presented by Ling-Fong Li at the International Symposium of Particle Theory and Phenomenology, Ames, Iowa, May 22-24, 199