Axiomatic quantum field theory

Wightman axioms

In mathematical physics, the Wightman axioms (also called Gårding–Wightman axioms), named after Arthur Wightman, 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 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. (Wikipedia).

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Zermelo Fraenkel Introduction

This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra

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From playlist Logic

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Set Theory (Part 2): ZFC Axioms

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Axioms of Lie algebra theory

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From playlist Algebra

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Zermelo Fraenkel Extensionality

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From playlist Algebra

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Related pages

Poincaré group | Four-vector | Effective field theory | Haag's theorem | Self-adjoint operator | Separable space | Yang–Mills existence and mass gap | Borchers algebra | Lorentz group | Cohomology | Light cone | Parastatistics | Constructive quantum field theory | Spin (physics) | Spontaneous symmetry breaking | Local quantum field theory | Unitary operator | Millennium Prize Problems | Ultraviolet divergence | Principle of locality | John von Neumann | Minkowski space | Wigner's theorem | Cutoff (physics) | Unbounded operator | Distribution (mathematics) | Euclidean space | Axiomatic quantum field theory | Four-momentum | Special linear group | Hilbert space | Projective representation | Weak topology | Cluster decomposition | Wigner's classification | Anyon | Unitary representation