Acerbi, F.; Morchio, G.; Strocchi, F. Algebraic fermion bosonization. (English) Zbl 0769.47023 Lett. Math. Phys. 26, No. 1, 13-22 (1992). The authors provide an algebraic fermion bosonization procedure including two steps.First of all they construct anticommuting fields out of infrared extended Bose fields in the framework of canonical extensions of C.C.R. algebras and of their non regular representations.Then, in a second step, they construct local Fermi fields as ultrastrong limits of bosonic variables in all representations which are locally Fock with respect to the ground state representation of the massless scalar field, so that, in particular, the algebraic operations commute with such limits.Recall that such a procedure was usually performed by strong limits on a dense set of states of specific bosonic models. Reviewer: G.Loupias (Montpellier) Cited in 5 Documents MSC: 47N55 Applications of operator theory in statistical physics (MSC2000) 81T05 Axiomatic quantum field theory; operator algebras 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Keywords:algebraic fermion bosonization procedure; anticommuting fields out of infrared extended Bose fields; canonical extensions of C.C.R. algebras; regular representations; local Fermi fields; ultrastrong limits of bosonic variables; representations which are locally Fock with respect to the ground state representation of the massless scalar field; strong limits on a dense set of states of specific bosonic models PDFBibTeX XMLCite \textit{F. Acerbi} et al., Lett. Math. Phys. 26, No. 1, 13--22 (1992; Zbl 0769.47023) Full Text: DOI References: [1] StreaterR. F., in C. P.Enz and J.Mehra (eds.), Physical Reality and Mathematical Description, D. Reidel, Dordrecht, 1974, pp. 375-386 and refs therein. [2] CareyA. L. and RuijsenaarsS. N. M., Acta Appl. Math. 10, 1 (1987). · Zbl 0644.22012 · doi:10.1007/BF00046582 [3] Acerbi, F., Master thesis, SISSA, October 1990; Acerbi, F., Morchio, G., and Strocchi, F., Infrared singular fields and non-regular representations of CCR algebras, preprint SISSA 39/92 FM; J. Math. Phys., in press, and Lett. Math. Phys., in press. [4] CareyA. L., RuijsenaarsS. N. M., and WrightJ. D., Comm. Math. Phys. 99, 347 (1985). · doi:10.1007/BF01240352 [5] MandelstamS., Phys. Rev. D 11, 3026 (1975). · doi:10.1103/PhysRevD.11.3026 [6] SkyrmeT. H. R., Proc. Roy. Soc. London Ser. A 247, 260 (1958). · doi:10.1098/rspa.1958.0183 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.