ghost field

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 transformations “gauge-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 October 12, 2017 15:45:54
by Urs Schreiber
(77.56.177.247)