growth conditions (E0'). Then one can appeal to the Osterwalder–Schrader theorem to show that Wightman functions are tempered distributions. Alternatively, and much easier, one can derive Wightman axioms directly from (OS0)-(OS4). Note however that the full quantum field theory will contain infinitely many other local operators apart from , such as , and other composite operators built from and its derivatives. It's not easy to extract these Schwinger functions from the measure and show that they satisfy OS axioms, as it should be the case. To summarize, the axioms called (OS0)-(OS4) by Glimm and Jaffe are stronger than the OS axioms as far as the correlators of the field are concerned, but weaker than then the full set of OS axioms since they don't say much about correlators of composite operators. Nelson's axioms These axioms were proposed by Edward Nelson. See also their description in the book of Barry Simon. Like in the above axioms by Glimm and Jaffe, one assumes that the field is a random distribution with a measure . This measure is sufficiently regular so that the field has regularity of a Sobolev space of negative derivative order. The crucial feature of these axioms is to consider the field restricted to a surface. One of the axioms is Markov property, which formalizes the intuitive notion that the state of the field inside a closed surface depends only on the state of the field on the surface. See also Wick rotation Axiomatic quantum field theory Wightman axioms References Axiomatic quantum field theory