1 - Sociedade Brasileira de Física

: from:
We need a better 0-order approximation to start
IV - Feynman - - Goldstone diagrams in a time - dependent basis
It is possible without changing much to extend
Feynthan-Goldstone perturbation theory to the case where
the basis is made up of time-dependent wave functions,all
being solutions of the same time-dependent Schrodinger-
equation.
That's our answer
Feynman diagrams with a time dependent basis:
= H o (t) + H 1 (t)
Feinman propagator K(t,t')
K(t,t')IT(t'); = 1,(t)3.
Feynman's decomposition (Feynman paths):
K(t,t') = lim K(t,t-c) K(t-c,t-20...K(t'+E,t')
C + 0 (N factors)
N + =
Nc = t-t'
K(T E,T ) ; 1-icH0 (r + c/2) - is H 1 (t + E/2)
= K o (T + c,T) - icH 1 (T + c/2)
to preserve unitarity in the unperturbed problem.
Collect terms according to their order in H 1 and
take the :limit:
K(t,t') = Ko(t,t1)-i dt i Ko (t,t 1 ) H 1 (t ) K o (tl' t') +
1
r
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