Faddeev-Popov Ghosts

Faddeev-Popov ghosts are mathematical tools used in quantum field theory, especially in gauge theories like quantum chromodynamics. They help correctly account for redundant variables (gauge symmetries) in calculations. When integrating over all possible configurations, these symmetries lead to overcounting, which ghosts correct by introducing additional, unphysical particles with peculiar properties—they don't appear directly in experiments but ensure the mathematics remains consistent and calculations yield accurate physical predictions. Essentially, they are a bookkeeping device that maintains the consistency and symmetry of the theory.