Functional-Equation Approach to Canonical Theories

We consider a possible formulation of canonical models in terms of a system of functional differential equations that the ground-state expectation functionals of exponentiated fields satisfy. We obtain these equations for the anharmonic oscillator in one-dimensional quantum mechanics and in a $\lambda {\phi }^4$ theory of self-interacting mesons in quantum field theory. We consider the implication of symmetries of the ground state on these functionals. We solve the system of functional equations for a free theory of scalar mesons, the case $\lambda =0\mathrm{}$.