Embedding Coordinates for the Well-Dressed Quark

Abstract

Traditional lore holds that there is only one way to represent local symmetry, leading to practically unique gauge theories. However there is more than one path to local symmetry. Here I discuss expressing the theory of dressed quarks, gluons and other particles using new variables. The gauge sector is expressed with fields e^a _μ which transform homogeneously like matter fields under the gauge group. Consistency requires further embedding in a larger global group. Many interesting topics of gauge theories, from the elementary nature of the Coulomb field to magnetic monopoles, serve as illustrations. Geometrical invariants forbidden in the standard coordinates become available in the new approach. I argue that these are natural, and useful, in the description of an effective theory. For example, in a covariant derivative expansion, one can express a massively propagating gauge invariant effective theory in four space-time dimensions.