Recent Developments in Gauge Theories pp 159-188 | Cite as

# Introduction to Lattice Gauge Theories

## Abstract

Since 1974 when K. Wilson^{[1]}proposed to study the large coupling behaviour of a Yang-Mills theory using a lattice to provide an ultraviolet cut-off, the literature on the subject has developped very fast. It is not however possible to claim at this moment that realistic answers have been provided to the central problem of quark confinement in quantum chromodynamics, including particle spectrum, partial conservation of the axial current... As it sometimes occur, certain aspects of questions have led to unexpected developments. The most striking is a closer relation between quantum field theory and statistical mechanics,including the behavior of disordered systems, the concept of frustration, dual transformations to describe new types of excitations... Numerical studies have been reported or are in progress. Together with various rigorous results they enable us to get a preliminary view of the phase diagram,particularly of the existence of transitions.

## Keywords

Gauge Theory Wilson Loop Ising Model Lattice Gauge Theory Dual Transformation## Preview

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## References

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- [18]It is interesting to quote the remarkable agreement between the Monte Carlo work and the analytical estimates obtained from strong coupling expansions both with an accuracy of a few percent at the present stage. Take for instance the self-dual 4-dimensional Z
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