The Euclidean theory can be formally defined as the theory which is obtained from the ordinary (pseudo-Euclidean) theory by the substitution t → −it. This substitution transforms the operator K in Eq. (1.2) into the Euclidean operator K e, and the quantum Schrödinger equation becomes an equation of the heat-conduction type: i∂ t ψ = Hψ → −∂ t ψ = Hψ (it is assumed that H does not depend explicitly on time).