INVARIANT STRUCTURES IN GAUGE THEORIES AND CONFINEMENT

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Abstract
The problem of finding all gauge invariants is considered in connection with the problem of confinement. Polylocal gauge tensors are introduced and studied. It is shown (both in physical and pure geometrical approaches) that the path-ordered exponential is the only fundamental bilocal gauge tensor, which means that any irreducible polylocal gauge tensor is built of P-exponentials and local tensors (matter fields). The simplest invariant structures in electrodynamics, chromodynamics and a theory with the gauge group SU(2) are considered separately. As a consequence of gauge invariance any “elementary” charge is accompanied by an external static field located on the integration contour of a P- exponential, i.e. by a string. The Coulomb field is analyzed from this point of view; it is demonstrated that it can also be considered as made of exponential line integrals. In QCD strings can branch—it means that the interquark static field cannot be associated with a simple P-exponential. On the contrary, in pure gluodynamics strings do not branch. Different forms of confinements are briefly reviewed.

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