We explain elementary arithmetic of Dirichlet quadratic forms on 3-dim lattice
(Feynman Kac formulas for Coulomb potentials) and apply it to investigation of expansions
(based on Wick formulas for polynomial, and also nonpolynomial, perturbations)
around corresponding gaussian fields. We suggest an example of a single spin
potential, written as suitable Laplace transform, for which the expansion can
be "renormalized" - suitably grouped together - to make its terms (indexed by
"conglomerates" of closed paths in underlying lattice) absolutely summable.
We compare it to the case of perturbative pair interactions, which has a different nature.