In quantum physics, unitarity is a restriction on the allowed evolution of quantum systems that ensures the sum of probabilities of all possible outcomes of any event is always 1.

More precisely, the operator which describes the progress of a physical system in time must be a unitary operator. When the Hamiltonian is time-independent the unitary operator is e^{-i \hat{H} t}.

Similarly, the S-matrix that describes how the physical system changes in a scattering process must be a unitary operator as well; this implies the optical theorem.

In quantum field theory one usually uses a mathematical description which includes unphysical fundamental particles, such as longitudinal photons. These particles must not appear as the end-states of a scattering process. Unitarity of the S-matrix and the optical theorem in particular implies that such unphysical particles must not appear as virtual particles in intermediate states. The mathematical machinery which is used to ensure this includes gauge symmetry and sometimes also Faddeev–Popov ghosts. (Sources: 1, 2 / Greek: Μοναδιστικό αξίωμα. Greek sources: 3, 4, 5)

In physics, Faddeev–Popov ghosts (also called ghost fields) are additional fields which are introduced into gauge quantum field theories to maintain the consistency of the path integral formulation. They are named after Ludvig Faddeev and Victor Popov. (6)

Quantum mechanics.

Full of axioms and meaningless notions!
Full of things that we KNOW they cannot exist and yet they are used in order to make the axioms work!

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