---------------------
Why Feynman diagrams?
---------------------
Feynman diagrams resemble processes with particles moving in space and
time, and are often figurately treated as such. But in fact they
do _not_ describe such processes, but certain multiple integrals.
(To emphasize this, the particles involved in Feynman diagrams are
called 'virtual particles' - except for the lines sticking out; these
are real particles to be prepared or observed. (Still, many people
think mistakenly that virtual particles are somehow also real. See the
entries about virtual particles elsewhere in this FAQ.)
Although it is nowhere said explicitly, Feynman diagrams are just
a mnemonic for nicely picturing the composition of higher order tensors.
Create for each tensor of a theory a different vertex type, draw a
vertex of this type for each occurence of this tensor in a product
expression in Einstein summation convention, and draw a line between
two such vertices whenever they share an index to be summed over.
The form of the lines defines the value of the coefficient function
in such a product, and the sum over Feynman diagrams simply means that
one considers a linear combination of these products, integrated over
the arguments. Thus this defines a generic representation of an
expansion of a function of the tensors of the theory.
Tuus Feynman diagrams can be used whenever one expands a function of one
or more tensors into a linear combination of products of components of
these tensors.
Indeed, for this reason, they are also used in classical statistical
mechanics and in the analysis of stochastic differential equations
by functional integration techniques.