Unitarity (physics)

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In quantum physics, unitarity means that the sum of probabilities of all possible outcome of any event is always 1. This is necessary for the theory to be consistent.

This implies that the operator which describes the progress of a physical system in time must be a unitary operator. This operator is $e i H t$ , where $H$ is the Hamiltonian of the system and $t$ is time.

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 a 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.

Since unitarity of a theory is necessary for its consistency, the term is sometimes also used as a synonym for consistency, and is sometimes used for other necessary conditions for consistency, in particular the condition that the Hamiltonian is bounded from below. This means that there is a state of minimal energy (called the ground state or vacuum state). This is needed for the second law of thermodynamics to hold.