Faddeev–Popov ghost

Ghost fields are unphysical fields that occur in the quantization of gauge theories in the path integral formalism. They are named after Ludwig Faddejew and Victor Popov, but were first used by Richard Feynman in gauge theories.

This " spirit boxes " ( ghosts ) are relics of the mathematical treatment of the non -Abelian gauge theories (Yang -Mills theory). In the path integral is integrated over all vector potentials, ie even those that are due to the " gauge freedom " equivalent. This " too much count " is compensated for in the formalism of Faddejew Popov and by introducing new fields, the ghosts, again. The mind fields appear only in closed loops of the Feynman diagrams, where they pick up the contribution of the "surplus" degrees of freedom of the vector potentials. All they need, although they in the case of Yang-Mills gauge theories complex scalar fields are (the index a refers to their color degrees of freedom, ie, values ​​in the adjoint representations of the gauge group as that of the vector potential fields) obey a fermionic statistics, so that the loop diagram a the contribution the ( according to the statistics bosonic ) vector fields opposite amount results. So you formally violate the spin- statistics theorem, but this does not matter because they do not correspond to physical particles.

In Yang-Mills fields ( such as quantum chromodynamics, see the specified there Lagrange density ) is their contribution to the Lagrangian:

For abelian gauge theories such as quantum electrodynamics, where is " decouple " the spirit fields and do not contribute.

Swell

• Quantum field theory