# What are Wightman fields/functions

Simple question: What are Wightman fields? What are Wightman functions? What are their uses? For example can I use them in operator product expansions? How about in scattering theory?

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Ok, so based on my reading, the field operators of a theory are understood to be distribution-valued, that is, to be integrated over a smooth function: e.g. $\hat\phi(f)\equiv\int dx f(x)\hat\phi(x)$. But if the smooth function has support over such a large region in space-time that if I try to compute time-ordered products, I run into some ambiguity. How do I define the time-ordering symbol for Wightman functions? –  QuantumDot Nov 17 '12 at 22:23