Wightman axioms

Summary

The Wightman axioms are a mathematically precise list of properties that a relativistic quantum field theory should have. They ask for a Hilbert space with a unitary representation of the Poincaré group, positive energy, and a unique invariant vacuum. The fields are operator-valued tempered distributions, covariant under the Poincaré group and commuting at spacelike separation. From them one proves general theorems such as the CPT theorem and the spin–statistics theorem. The vacuum expectation values of products of fields, the Wightman functions, determine the whole theory.