[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

No abstract available

[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)

[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)

[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

[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

[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)

[en] A general method is proposed for the operator quantization of relativistic dynamical systems with first-class constraints

[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.

[en] We give some examples of the problems where non-Hilbert spaces could be relevant.