Point-particle Faddeev–Popov ghost action ($S_{\mathrm{gh}}=\int ib\dot{c}dt$)

For a relativistic particle, the Hamiltonian gauge parameter changes the worldline einbein by its time derivative. Fixing the einbein to a constant therefore gives a Faddeev-Popov determinant of ${\partial }_t$, represented by anticommuting FP ghosts. Gauge zero modes and the proper-time modulus are treated separately. The displayed phase convention gives the odd canonical bracket $\{b,c\}=-i$.