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Mathematical Proceedings of the Cambridge Philosophical Society, 1926
For the purposes of atomic physics it has been found convenient to introduce the idea of quantities that do not in general satisfy the commutative law of multiplication, but satisfy all the other laws of ordinary algebra.
P. Dirac
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For the purposes of atomic physics it has been found convenient to introduce the idea of quantities that do not in general satisfy the commutative law of multiplication, but satisfy all the other laws of ordinary algebra.
P. Dirac
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Mathematical aspects of the operator algebraic approach to quantum field theory
2023Im 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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Некоторые алгебраические и геометрические аспекты квантовых измерений
Труды Математического института имени В. А. Стеклова, 2021С помощью алгебраических и геометрических методов изучаются положительные операторнозначные меры. Доказано, что эти меры можно параметризовать с помощью некоторого пуассонова многообразия. Также показано, как получить симплектические листы данного пуассонова многообразия в терминах параметров этих мер.
Ilya Zhdanovskiy +2 more
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Пределы индуктивных последовательностей алгебр Теплица-Кунца
Труды Математического института имени В. А. Стеклова, 2021Рассматриваются индуктивные последовательности алгебр Теплица-Кунца. Связующие гомоморфизмы такой последовательности определяются конечным набором последовательностей натуральных чисел. Доказывается, что индуктивный предел такой последовательности алгебр Теплица-Кунца изоморфен редуцированной полугрупповой $C^*$-алгебре, построенной для унитализации ...
Suren Arshakovich Grigoryan +2 more
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, 2019
Unique in its clarity, examples, and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research.
K. Cahill
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Unique in its clarity, examples, and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research.
K. Cahill
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Quantum Holonomies from Spectral Networks and Framed BPS States
, 2016We propose a method for determining the spins of BPS states supported on line defects in 4d $${\mathcal{N}=2}$$N=2 theories of class S. Via the 2d–4d correspondence, this translates to the construction of quantum holonomies on a punctured Riemann surface
Maxime Gabella
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Communications in Mathematical Physics, 2017
We introduce the natural (t, q)-deformation of the Q-system algebra in type A. The q-Whittaker limit $$t\rightarrow \infty $$t→∞ gives the quantum Q-system algebra of Di Francesco and Kedem (Lett Math Phys 107(2):301–341, [DFK17]), a deformation of the ...
P. Di Francesco, R. Kedem
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We introduce the natural (t, q)-deformation of the Q-system algebra in type A. The q-Whittaker limit $$t\rightarrow \infty $$t→∞ gives the quantum Q-system algebra of Di Francesco and Kedem (Lett Math Phys 107(2):301–341, [DFK17]), a deformation of the ...
P. Di Francesco, R. Kedem
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, 2017
The ideas of noncommutative geometry are deeply rooted in both physics, with the predominant influence of the discovery of Quantum Mechanics, and in mathematics where it emerged from the great variety of examples of “noncommutative spaces” i.e.
A. Connes
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The ideas of noncommutative geometry are deeply rooted in both physics, with the predominant influence of the discovery of Quantum Mechanics, and in mathematics where it emerged from the great variety of examples of “noncommutative spaces” i.e.
A. Connes
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Fundamental Mathematical Structures of Quantum Theory
2019This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including
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