Relation to tree diagramms
Perturbative solutions of classical field equations
Amputation of the last leg
Perturbative solutions of classical field equations
Let us take 
to be the space of perturbative solutions 
of nonlinear equations of the form:
to be the space of perturbative solutions of nonlinear equations of the form:
where 
is some linear differential operator, and 
is a nonlinear function
describing the interaction. We assume that 
is a polynomial starting with
quadratic or higher order terms.
is some linear differential operator, and is a nonlinear function
describing the interaction. We assume that is a polynomial starting with
quadratic or higher order terms.The point 
will be the zero solution 
.
Then 
can be identified with the space of solutions of
the linearized equation:
will be the zero solution .
Then can be identified with the space of solutions of
the linearized equation:
Tree level perturbation theory can be thought of as a 1-parameter map
|
where 
satisfies:
satisfies:
The definitions of the operator has an ambiguity
(because one can add a solution of the free equation).
Suppose that we made some choice of .
has an ambiguity
(because one can add a solution of the free equation).
Suppose that we made some choice of .Amputation of the last leg
Let us define 
as follows:
as follows:
