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. IvanovAtominstitut 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 )
Abstract
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
