Damaskinskij, E. V. Spontaneously broken phase and Galilei transformations in Weyl systems. (Russian. English summary) Zbl 0569.22022 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 145, 72-85 (1985). Representation in Hilbert bundle of covariant Weyl systems with spontaneous breakdown of symmetry is discussed. Equivalence of direct integral realizations of covariant Weyl systems with representation in the space of the sections of the Hilbert bundle is established. Spontaneous breakdown of phase transformations for the Weyl systems, realized by Hilbert bundle representation, is investigated. Generalized (after Rocca and Sirigue) phase operators and phase states are constructed in this formalism. Cited in 1 Review MSC: 22E70 Applications of Lie groups to the sciences; explicit representations 81R40 Symmetry breaking in quantum theory Keywords:Hilbert bundle; covariant Weyl systems; spontaneous breakdown of symmetry; phase operators PDFBibTeX XMLCite \textit{E. V. Damaskinskij}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 145, 72--85 (1985; Zbl 0569.22022) Full Text: EuDML