THE GOLDSTONE THEOREM AT 2 LOOPS FROM AN ALGEBRAIC IDENTITY

We give an explicit demonstration of the Goldstone theorem at the leve l of two-loop Feynman graphs in the spontaneously broken O(2) linear s igma model by showing that the integrands of the 1PI ''pion'' self-ene rgy graphs cancel each other at zero momentum as a consequence of the identity m(2)[k(2)(k(2)+m(2))](-1)=k(-2)-(k(2)+m(2))(-1). The proof ho lds for any regularization scheme which respects this identity.