An Introduction to Lattice Gauge Theories

Abstract

By studying the renormalized perturbation theory of ordinary continuous gauge theories which corresponds to the classical lagrangian L:

$$ L = \frac{1}{{4g_0^2}}{\vec F_{\mu \nu }}{\vec F_{\mu \nu }},{\vec F_{\mu \nu }} = {\partial _\mu }{\vec A_\nu } - {\partial _\nu }{\vec A_\mu } + {\vec A_\mu } \times {\vec A_\nu }, $$

(1)

we learn from renormalized group arguments that the theory is simple at short distance, and complicated at long distance where the effective coupling constant becomes large. Therefore the perturbative spectrum of the theory which consists of massless vector mesons may not be the true spectrum of the theory.