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For a given base space $M$ (spacetime), we consider the Guichardet space overthe Guichardet space over $M$. Here we develop a ''field calculus'' based onthe Guichardet integral. This is the natural setting in which to describe Greenfunction relations for Boson systems. Here we can follow the suggestion ofSchwinger and develop a differential (local field) approach rather than theintegral one pioneered by Feynman. This is helped by a DEFG(Dyson-Einstein-Feynman-Guichardet) shorthand which greatly simplifiesexpressions. This gives a convenient framework for the formal approach ofSchwinger and Tomonaga as opposed to Feynman diagrams. The Dyson-Schwinger isrecast in this language with the help of bosonic creation/annihilationoperators. We also give the combinatorial approach to tree-expansions.

Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams