# Wightman axioms ## Refs [Wiki](https://en.wikipedia.org/wiki/Wightman_axioms) [nLab](https://ncatlab.org/nlab/show/Wightman+axioms) [Notes by Robert](https://zmp.math.uni-hamburg.de/robert_zmp_qft.pdf) ## Remarks - these are defined for ==Minkowski== QFTs. A corresponding set of conditions/axioms in Euclidean space are given in [[0112 Osterwalder-Schrader reconstruction theorem]] - quantum mechanical in nature ## Wightman axioms ###### As given in [[1973#Osterwalder, Schrader]] - R0: Temperedness - R1: Relativistic invariance - R2: Positivity - R3: Local commutativity - R4: Cluster property - R5: Spectral conditions ###### As given in [[Rsc0014 Rychkov TASI2019 Lorentzian CFT]] ![[Rsc0014 Rychkov TASI2019 Lorentzian CFT#QFT Wightman Axioms]]