# Contents

## Idea

In gauge theory the configuration space/phase space is not in general a smooth space, but a smooth groupoid: the gauge transformations between gauge fields are the morphisms of this groupoid.

The infinitesimal approximation to this smooth groupoid is a Lie algebroid. The dg-algebra of functions on this is called the BRST complex of the gauge theory. It contains in degree-0 the (duals to) the gauge fields and in degree-1 the cotangents to the gauge transformations. These degree-1 elements that appear here alongside the physical fields in degree 0 are called ghost fields in the physics literature.

If there are higher gauge transformationsgauge-of-gauge transformations” then the BRST complex has generators in higher degree, too, the cotangents to these higher gauge transformations. These are then called ghost-of-ghost fields.

For more details and further pointers see at BRST complex and in particular at BV-BRST formalism.

Revised on January 18, 2015 23:29:53 by Urs Schreiber (88.100.66.95)