Goldstone Theorem in the Gaussian Functional Approximation to the Scalar   $\phi^{4}$ Theory
  We verify the Goldstone theorem in the Gaussian functional approximation to the $\phi^{4}$ theory with internal O(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. 
V. Dmitra\v{s}inovi\'c, J.R. Shepard and J.A. McNeil