article “ There are no Goldstone Bosons in Two Dimensions ”

We discuss Coleman’s theorem asserting the absence of a spontaneously broken continuous symmetry and Goldstone bosons in the quantum field theory of a free massless (pseudo)scalar field in 1+1–dimensional space–time (Comm. Math. Phys. 31, 259 (1973)). We show that Coleman’s theorem is erroneous. We prove that the main signature for the absence of Goldstone bosons, a vacuum state, invariant under the continuous symmetry, does not exist in the quantum field theory of a free massless (pseudo)scalar field in 1+1–dimensional space–time. E–mail: [email protected], Tel.: +43–1–58801–14261, Fax: +43–1–5864203 E–mail: [email protected], Tel.: +43–1–58801–14261, Fax: +43–1–5864203 Permanent Address: State Technical University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation