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The discrete quantum origin of the Lorentz group and the $Z_3$-graded ternary algebras (Mathematical aspects of quantum fields and related topics)

The discrete quantum origin of the Lorentz group and the $Z_3$-graded ternary algebras (Mathematical aspects of quantum fields and related topics)
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The Arcsine Law and "Quantum-Classical Correspondence" (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)

The Arcsine Law and "Quantum-Classical Correspondence" (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)
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Application of Resolvent CCR Algebras to Statistical Mechanics of Bosons on Lattices (Mathematical Aspects of Quantum Fields and Related Topics)

Application of Resolvent CCR Algebras to Statistical Mechanics of Bosons on Lattices (Mathematical Aspects of Quantum Fields and Related Topics)
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APPLICATIONS OF FREE PROBABILITY TO QUANTUM INFORMATION THEORY (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)

APPLICATIONS OF FREE PROBABILITY TO QUANTUM INFORMATION THEORY (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)
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Mathematical aspects of the operator algebraic approach to quantum field theory

2023
Im ersten Kapitel rekonstruieren wir die algebraische Quantentheorie und beweisen Sakais Charakterisierung von von-Neumann-Algebren, wobei wir dem Ansatz von Takesaki und Tomiyama folgen. Im zweiten Kapitel betrecten wir zusätzliche Beschränkungen aus der Relativitäts theorie die Objekte der Quantentheorie fest und untersuchen die Konsequen- zen ...
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Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics

Theoretical and Mathematical Physics, 1988
A new and extremely important property of the algebraic structure of symmetries of nonlinear infinite-dimensional integrable Hamiltonian dynamical systems is described. It is shown that their invariance groups are isomorphic to a unique universal Banach Lie group of currents \(G={\mathcal S}\odot Diff(T^ n)\) on an n-dimensional torus \(T^ n ...
Bogolyubov, N. N. jun., Prikarpatskij, A. K.   +1 more
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Quantum Algebras and Poisson Geometry in Mathematical Physics

2005
Noncommutative algebras, nanostructures, and quantum dynamics generated by resonances by M. Karasev Algebras with polynomial commutation relations for a quantum particle in electric and magnetic fields by M. Karasev and E. Novikova Poisson structures and linear Euler systems over symplectic manifolds by Y. Vorobjev Poisson equivalence over a symplectic
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Algebras of unbounded operators and vacuum superselection rules in quantum field theory

Theoretical and Mathematical Physics, 1984
The algebraic structure of quantum-field systems with vacuum superselection rules is analyzed in the framework of Wightman axiomatics on the basis of the mathematical formalism developed in Part I [ibid. 59, 28-48 (1984; Zbl 0559.47033)]. Two main theorems are obtained.
Voronin, A. V., Sushko, V. N., Khoruzhij, S. S.   +2 more
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Quantum Computing Techniques for Numerical Linear Algebra in Computational Mathematics

Panamerican Mathematical Journal
Quantum computing is a new and exciting area of computational mathematics that has the ability to solve very hard problems that traditional computing methods have not been able to solve for a long time. This abstract goes into detail about how quantum computing can be used in numerical linear algebra, which is an important part of computational ...
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Mathematical Modelling of Quantum Information Systems Using Operator Algebra Techniques

International Journal of Mathematical Analysis and Research
Quantum information theory has become a central area in the two fields of quantum mechanics and information science. The focus of this work is mathematical modelling of quantum information with the use of operator algebras, in a way that accentuates the modelling, and acting or manipulation of observables and quantum states.
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