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Particles and Fields

Eur. Phys. J. C 24, 653-663 (2002)
DOI: 10.1007/s10052-002-0966-2

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

M. Faber and A.N. Ivanov

Atominstitut der Österreichischen Universitäten, Arbeitsbereich Kernphysik und Nukleare Astrophysik, Technische Universität Wien, Wiedner Hauptstr. 8-10, 1040 Wien, Österreich

(Received: 19 December 2001 / Revised version: 31 March 2002 / Published online: 14 June 2002 )

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 in such a quantum field theory (i) a continuous symmetry of (pseudo)scalar field translations is spontaneously broken, (ii) Goldstone bosons appear as quanta of a free massless (pseudo)scalar field and (iii) there is a non-vanishing spontaneous magnetization. In spite of the existence of a spontaneous magnetization the main inequality between vacuum expectation values of certain operators which have been used for the derivation of the Mermin-Wagner-Hohenberg theorem (C. Itzykson and J.-M. Drouffe, Statistical field theory, Vol. I, 1989, pp. 219-224) is fulfilled.

© Società Italiana di Fisica, Springer-Verlag 2002

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