The gauge technique

The gauge technique is a nonperturbative scheme for solving the field equations in gauge theories. This thesis is devoted towards understanding and extending the approximation procedures in the gauge technique. In the past the lowest order approximation consisted in only taking into account the longitudinal amplitudes; we have succeeded in generalizing it to incorporate transverse corrections for arbitrary covariant gauges in the context of electrodynamics. As a consequence the nonperturbative results are exact to order e 4 , and the gauge invariance of the vacuum polarization is correspondingly restored by the refined technique. Contrary to common belief, we have also found that the radiative corrections to the gluon propagator lie solely in the contributions of transverse vertices. Thus in principle the lowest order gauge technique is not readily applicable to the gluon sector of quantum chromodynamics. Finally we have shown that in two-dimensional electrodynamics (massless Schwinger model) the gauge technique produces exact results because one is able to solve the vector and axial Ward-Takahashi identities uniquely. In this way it is possible to obtain the complete solution for any linear gauge at any temperature.