In physics the Wightman axioms are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s but they were first published only in 1964, after Haag-Ruelle scattering theory affirmed their significance.
The axioms exist in the context of constructive quantum field theory, and they are meant to provide a basis for rigorous treatment of quantum fields, and strict foundation for the perturbative methods used. One of the Millennium Problems is to realize the Wightman axioms in the case of Yang-Mills fields.
Read more about Wightman Axioms: Rationale, Consequences of The Axioms, Relation To Other Frameworks and Concepts in Quantum Field Theory, Existence of Theories Which Satisfy The Axioms
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