0 v 1 2 2 M ar 1 99 9 A Critique of the Gauge Technique

A summary of the successes of and obstacles to the gauge technique (a non-perturbative method of solving Dyson-Schwinger equations in gauge theories) is given, as well as an outline of how progress may be achieved in this field. 1 The gauge technique Nature seems inordinately fond of gauge theories. Chromodynamics, elec-troweak theory and gravitation are all based on the gauge principle, featuring the groups SU(3), SU(2)×U(1) and SL(2,c), respectively. It is quite likely that any unified gauge model of the fundamental forces will also be a gauge field theory and it is conceivable that a supersymmetric version, in some higher dimension, will be founded on a local supergauge principle, although nature seems reticent to display her supersymmetric hand in the low energy spectrum of states. Whenever a field theory is invariant under local group transformations, the resulting Green functions obey a series of 'gauge covariance' relations which specify how the functions change under a variation of gauge 1. In QED these relations were originally found by Landau and Khalatnikov (1956, LK 1 Purely photonic processes and amplitudes involving on-shell fermions remain gauge-invariant of course.