6 research outputs found
A study of Schwinger-Dyson Equations for Yukawa and Wess-Zumino Models
We study Schwinger-Dyson equation for fermions in Yukawa and Wess-Zumino
models, in terms of dynamical mass generation and the wavefunction
renormalization function. In the Yukawa model with -type interaction
between scalars and fermions, we find a critical coupling in the quenched
approximation above which fermions acquire dynamical mass. This is shown to be
true beyond the bare 3-point vertex approximation. In the Wess-Zumino model,
there is a neat cancellation of terms leading to no dynamical mass for
fermions. We comment on the conditions under which these results are general
beyond the rainbow approximation and also on the ones under which supersymmetry
is preserved and the scalars as well do not acquire mass. The results are in
accordance with the non-renormalization theorem at least to order in
perturbation theory. In both the models, we also evaluate the wavefunction
renormalization function, analytically in the neighbourhood of the critical
coupling and numerically, away from it.Comment: 12 pages and 7 Postscript figures, accepted for publication in
Journal of Physics G: Nuclear and Particle Physic
Anomalies without Massless Particles
Baryon and lepton number in the standard model are violated by anomalies,
even though the fermions are massive. This problem is studied in the context of
a two dimensional model. In a uniform background field, fermion production
arise from non-adiabatic behavior that compensates for the absence of massless
modes. On the other hand, for localized instanton-like configurations, there is
an adiabatic limit. In this case, the anomaly is produced by bound states which
travel across the mass gap. The sphaleron corresponds to a bound state at the
halfway point.Comment: (26 pages, 3 figures, uses harvmac and uufiles), UCSD/PTH 93-3