Goldstone theorem in the Gaussian functional approximation to the scalarφ4 theory

We verify the Goldstone theorem in the Gaussian functional approximation to theφ4 theory with internalO(2) symmetry. We do so by reformulating the Gaussian approximation in terms of Schwinger-Dyson equations from which an explicit demonstration of the Goldstone theorem follows directly. Axial current conservation is also shown to hold.