Generalized Calculation of Path Integrals for Quadratic Form Actions: Some Questions

[Jay R. Yablon]

In an exercise linked at:

http://jayryablon.files.wordpress.com/2009/11/exact-closed-form-calculation-for-quadratic-form-path-integrals.pdf

I have sought to examine the mathematics used to obtain a closed form
expression for the path integral for a Lagrangian which is a general
polynomial in the field psi, for any and all orders in the field, but
with the constraint that the Lagrangian include terms which are
quadratic in the field, i.e., that it include terms

.5K psi^2 + J psi (1)

I would appreciate feedback, particularly about (2.18) in this exercise,
whether this general form is known (I find it hard to think that it is
not), and if so, how this form is generally talked about in relation to
"perturbation theory."

Thanks,

Jay
____________________________
Jay R. Yablon
Email: jya...@nycap.rr.com
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