  A pedagogical introduction to the theory of a gaussian scalar field which
shows firstly, how the whole theory is encapsulated in the Wightman function
$W(x,y)=\langle\phi(x)\phi(y)\rangle$ 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".
