On free massless (pseudo)scalar quantum field theory in 1+1–dimensional space–time

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1–dimensional space–times free of infrared divergences. We show that a continuous symmetry of (pseudo)scalar field translations is spontaneously broken. Goldstone bosons appear as quanta of a free massless (pseudo)scalar field. We show that the main inequality between vacuum expectation values of certain operators which has been used for the derivation of the Mermin–Wagner–Hohenberg theorem is fulfilled in the the quantum field theory a free massless (pseudo)scalar field free of infrared divergences. 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 1