LAUSR

A pedagogical introduction to the theory of a Gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function rW(x,y) = 〈ϕ(x)ϕ(y)〉 regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at W(x,y) starting from nothing but the retarded Green function G(x,y). Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished “vacuum” or “ground state”, and to recognize some interesting formal relationships, including a general condition on W(x,y) expressing zero-entropy or “purity”.