491 research outputs found
Field Calculus:Quantum and Statistical Field Theory without the Feynman Diagrams
For a given base space (spacetime), we consider the Guichardet space over
the Guichardet space over . Here we develop a ''field calculus'' based on
the Guichardet integral. This is the natural setting in which to describe Green
function relations for Boson systems. Here we can follow the suggestion of
Schwinger and develop a differential (local field) approach rather than the
integral one pioneered by Feynman. This is helped by a DEFG
(Dyson-Einstein-Feynman-Guichardet) shorthand which greatly simplifies
expressions. This gives a convenient framework for the formal approach of
Schwinger and Tomonaga as opposed to Feynman diagrams. The Dyson-Schwinger is
recast in this language with the help of bosonic creation/annihilation
operators. We also give the combinatorial approach to tree-expansions
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