## Digitized Theses

1988

Dissertation

#### Degree Name

Doctor of Philosophy

#### Abstract

The operator-product expansion will be applied to the two-point Green functions of QCD in order to study the dynamical generation of quark masses. The lowest order quark and gluon condensate contributions to the quark self-energy will be calculated to all orders in the expansions of the quark-quark and gluon-gluon vacuum expectation values. The resulting on-shell gauge independence of the quark self-energy leads self-consistently to a non-perturbative dynamical quark mass in agreement with the phenomenology of up and down constituent mass.;The order g{dollar}\sp3{dollar}, chiral-violating, mixed condensate component of the quark self-energy will be calculated to order m{dollar}\sp3{dollar} in the expansions of the quark-quark and quark-gluon-quark vacuum expectation values, and then extended to all orders. The resulting self-energy is gauge independent for arbitrary values of the current mass, and the pole position of the quark propagator is unshifted from the value obtained from the quark and gluon condensates.;The lowest order quark condensate projection of the gluon propagator will be calculated to all orders in the quark-quark vacuum expectation value. The self-energy is found to be transverse, satisfying the Slavnov-Taylor identity. Implications for mechanisms which lead to an effective gluon mass will be considered. A brief application of this result to the QCD sum rule for the {dollar}\rho{dollar} meson will also be presented.

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