ghost field

**standard model of particle physics**

**matter field fermions** (spinors, Dirac fields)

1st | 2nd | 3d |
---|---|---|

up? | charm | top |

down? | strange? | bottom |

**hadron** (bound states of the above quarks)

**minimally extended supersymmetric standard model**

bosinos:

**dark matter candidates**

**Exotica**

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*.

Last revised on December 9, 2017 at 10:05:57. See the history of this page for a list of all contributions to it.