Unitarity

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 always equals 1.

Since unitarity of a theory is necessary for its consistency (it is a very natural assumption, although recently questioned), the term is sometimes also used as a synonym for consistency, and is sometimes used for other necessary conditions for consistency, especially 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 third law of thermodynamics to hold.

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.

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 ${\displaystyle e^{-i{\hat {H}}t/\hbar }}$.

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