Abstract
We give a complete description of the states of the C.C.R. algebra for a finite number of degrees of freedom which are invariant with respect to subgroups of the translation group of phase space. We make precise some well-known results of quantum mechanics such as Bloch theorem.
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Sirugue, M.: Improper states of canonical communication relation for a finite number of degrees of freedom. Preprint, Marseille (1971)
Manuceau, J.: Ann. Inst. Henri PoincaréVIII (2), 139 (1968)
Manuceau, J., Sirugue, M., Testard, D., Verbeure, A.: Commun. math. Phys.32, 231–243 (1973)
Slawny, J.: On factor representation and theC*-algebra of C.C.R. Preprint, Göttingen (1971)
Naimark, M.A.: Normed rings. Groningen: Wolters-Noordhoff Publishing 1970
Dixmier, J.: LesC*-algèbres et leurs représentations. Paris: Gauthier-Villars 1969
Kittel, C.: Introduction to solid state physics. New York: John Wiley-Sons 1959
von Naumann, J.: Math. Ann.104, 570 (1931)
Mackey, G.W.: Duke Math. J.16, 313–326 (1949)
Slawny, J.: On the regular representation, von Neumann uniqueness theorem and theC*-algebra of canonical commutation and anticommutation relations. Preprint, Tel Aviv (1971)
Zak, J.: Phys. Rev.168, 686 (1968)
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Communicated by H. Araki
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Beaume, R., Manuceau, J., Pellet, A. et al. Translation invariant states in quantum mechanics. Commun.Math. Phys. 38, 29–45 (1974). https://doi.org/10.1007/BF01651547
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DOI: https://doi.org/10.1007/BF01651547