Dissecting Ghosts?

Ghosts of ghosts for second class constraints

When one uses the Dirac bracket, second class constraints become first class. Hence, they are amenable to the BRST treatment characteristic of ordinary first class constraints. This observation is the starting point of a recent investigation by Batalin and Tyutin, in which all the constraints are put on the same footing. However, because second class constraints identically vanish as operators ...

Lecture Notes on Ghosts & Differential Ghosts

Lecture 10 on Differential Equations & Differential Invariants and Lecture 11 on Differential Equations & Proofs equipped us with powerful tools for proving properties of differential equations without having to solve them. Differential invariants (dI) [Pla10a, Pla12] prove properties of differential equations by induction based on the right-hand side of the differential equation, rather than i...

Ghosts of Company.

Living with Ghosts

Perturbation theory for gravity in dimensions greater than two requires higher derivatives in the free action. Higher derivatives seem to lead to ghosts, states with negative norm. We consider a fourth order scalar field theory and show that the problem with ghosts arises because in the canonical treatment, φ and 2φ are regarded as two independent variables. Instead, we base quantum theory on a...

Faddeev Popov Ghosts

These notes are to accompany my talk on gauge xing in quantum eld theories (QFTs), and the mathematical tricks associated with this procedure. In Section 1 I will look at gauge xing for Abelian elds, considering the speci c case of the Maxwell theory describing photons. In Section 2 I consider a non-Abelian generalization of the Maxwell theory called Yang Mills theory, which describes vector bo...