2002/04/29 by M. Faber, Faber, M., A. N. Ivanov +1
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0204237
27pages, Latex, no figures, title is changed and text is revised
openalex publication_date 2002/04/29 · arxiv created 2003/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse Coleman's theorem asserting the absence Goldstone bosons and spontaneously broken continuous symmetry 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 confirm that Coleman's theorem reproduces well-known Wightman's statement about the non-existence of a quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-time in terms of Wightman's observables defined on the test functions from S(R2). Referring to our results (Eur. Phys. J. C 24, 653 (2002)) we argue that a formulation of a quantum field theory of a free massless (pseudo)scalar field in terms of Wightman's observables defined on the test functions from S0(R2) is motivated well by the possibility to remove a collective zero-mode motion of the ``center of mass'' of a free massless (pseudo)scalar field (Eur. Phys. J. C 24, 653 (2002)) responsible for infrared divergences of the Wightman functions. We show that in the quantum field theory of a free massless (pseudo)scalar field with Wightman's observables defined on the test functions from S0(R2) a continuous symmetry is spontaneously broken. Coleman's theorem reformulated for the test functions from S0(R2) does not refute this result. We construct a most general version of a quantum field theory of a self-coupled massless (pseudo)scalar field with a conserved current. We show that this theory satisfies Wightman's axioms and Wightman's positive definiteness condition with Wightman's observables defined on the test functions from S(R2) and possesses spontaneously broken continuous symmetry. Nevertheless, in this theory the generating functional of Green functions exists only when the collective zero-mode is not excited by the external source.