  We define the combinatorial Dirichlet-to-Neumann operator and establish a
gluing formula for determinants of discrete Laplacians using a combinatorial
Gaussian quantum field theory. In case of a diagonal inner product on cochains
we provide an explicit local expression for the discrete Dirichlet-to-Neumann
operator. We relate the gluing formula to the corresponding Mayer-Vietoris
formula by Burghelea, Friedlander and Kappeler for zeta-determinants of
analytic Laplacians, using the approximation theory of Dodziuk. Our argument
motivates existence of gluing formulas as a consequence of a gluing principle
on the discrete level.
