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AbstractAbstract
[en] The authors show that the general linearity condition used to construct quantum operators, can be completed by a correspondence condition on dynamics. This leads to a non-linear equation for the quasi-probability operator, which determines every other quantum operator. The explicit form of this equation is then determined by the hamiltonian function of the system
[fr]
Les auteurs montrent que la condition generale de linearite pour la construction des operateurs quantiques peut etre completee par une condition de correspondance en dynamique. Ceci amene a une certaine equation non-lineaire pour l'operateur de la (quasi-)probabilite qui determine tous les autres operateurs quantiques. La forme explicite de l'equation mentionnee est, a son tour, determinee par la fonction d'Hamilton du systeme considereOriginal Title
Une equation pour l'operateur de la (quasi-)probabilite
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Journal Article
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Annales de la Fondation Louis de Broglie; v. 5(2); p. 105-109
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AbstractAbstract
No abstract available
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Journal Article
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Foundations of Physics; v. 4(1); p. 19-22
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Mitter, H.; Yamazaki, K.
Graz Univ. (Austria)1984
Graz Univ. (Austria)1984
AbstractAbstract
[en] An exponential of the sum of three operators can be factorized formally as a product of three exponentials, if the three operators form a closed algebra. (Author)
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Mar 1984; 4 p
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Report
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Yang, Xiangdong, E-mail: yangsddp@126.com2014
AbstractAbstract
[en] We study the inverse eigenvalue problem for the half-line random Schrödinger operators. Generalizing results from Miklòs Horvàth, we obtain optimal and almost optimal conditions for a set of eigenvalues to determine the random Schrödinger operator almost precisely. These conditions are simple closed properties of the random exponential system corresponding to the known eigenvalues. (papers)
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Available from http://dx.doi.org/10.1088/0266-5611/30/6/065009; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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Holten, J.W. van
Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H; NIKHEF-H-Stichting FOM Collaboration1990
Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H; NIKHEF-H-Stichting FOM Collaboration1990
AbstractAbstract
[en] The authors construct the BRST and anti-BRST operator for a compact Lie algebra which is a direct sum of abelian and simple ideals. Two different inner products are defined on the ghost space and the hermiticity propeties of the ghost and BRST operators with respect to these inner products are discussed. A decomposition theorem for ghost states is derived and the cohomology of the BRST complex is shown to reduce to the standard Lie-algebra cohomology. The authors show that the cohomology classes of the Lie algebra are given by all invariant anti-symmetric tensors and explain how thse can be obtained as zero-modes of an invariant operator in the representation space of the ghosts. Explicit examples are given. (author) 24 refs
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Feb 1990; 24 p
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Report
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Zachos, Cosmas K, E-mail: zachos@anl.gov2013
AbstractAbstract
[en] Ternary algebras amount to closing systems of antisymmetrized trinomials of operators. The Filippov conditions (FI, which are not identities) for ternary algebras are contrasted to Bremner's identities dictated by associativity of operator products, and thus analogous to Jacobi identities. Maps of the known FI-compliant ternary algebras to underlying classical Nambu brackets are constructed, which then explain this compliance: FI-compliant ternary algebras are essentially classical Nambu brackets in disguise. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal ternary algebra, and then explicitly realized through classical Nambu brackets. We illustrate this classical-contraction method on our Virasoro-Witt ternary algebra paradigm. The content of the talk is in the two references
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QTS6: 6. international symposium on quantum theory and symmetries; Lexington, KY (United States); 20-25 Jul 2009; Available from http://dx.doi.org/10.1088/1742-6596/462/1/012060; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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Conference
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Journal of Physics. Conference Series (Online); ISSN 1742-6596;
; v. 462(1); [1 p.]

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AbstractAbstract
[en] The mixing structure of a given quantum state (statistical operator) ρ is considered, that is, the pure states and associated weights of which it consists. Its influence on the state-dependent quantum logical implication determined by ρ is also studied. It is found that it has no influence at all except through the null-projector. It is shown that the latter, when it determines the state-dependent implication, in a certain sense, carries with it all the Boolean mathematical structure of projectors in the given Boolean subalgebra B of quantum logic P(H), where B is the 'domain' of definition of the state-dependent implication. (author)
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Available online at the Web site for the Journal of Physics. A, Mathematical and General (ISSN 4361-6447) http://www.iop.org/; Country of input: Argentina
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Journal Article
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Journal of Physics. A, Mathematical and General; ISSN 0305-4470;
; v. 29(2); p. 467-469

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AbstractAbstract
[en] A general method is proposed for the operator quantization of relativistic dynamical systems with first-class constraints
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Cover-to-cover translation of Yadernaya Fizika (USSR).
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Bai, Liqian; Chen, Xueqing; Ding, Ming; Xu, Fan, E-mail: bailiqian@nwpu.edu.cn, E-mail: chenx@uww.edu, E-mail: m-ding04@mails.tsinghua.edu.cn, E-mail: fanxu@mail.tsinghua.edu.cn2018
AbstractAbstract
[en] We define a quantum analog of a class of generalized cluster algebras which can be viewed as a generalization of quantum cluster algebras defined in Berenstein and Zelevinsky (Adv. Math. 195(2), 405–455 2005). In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in Chekhov and Shapiro (Int. Math. Res. Notices 10, 2746–2772 2014) and Rupel (2013) to the quantum case.
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Copyright (c) 2018 Springer Nature B.V.; Article Copyright (c) 2017 Springer Science+Business Media B.V.; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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Algebras and Representation Theory; ISSN 1386-923X;
; v. 21(6); p. 1203-1217

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Belokurov, V. V.; Shavgulidze, E. T., E-mail: vvbelokurov@yandex.ru2017
AbstractAbstract
[en] We give some examples of the problems where non-Hilbert spaces could be relevant.
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Copyright (c) 2017 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)
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