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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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Quantum Computing Techniques for Numerical Linear Algebra in Computational Mathematics
Panamerican Mathematical JournalQuantum 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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Rolandion Algebra as a Mathematically Rigorous Framework for Quantum Gravity
We present Undecion (or Rolandion) Algebra, a mathematically rigorous 11-dimensional algebraic framework designed to bridge quantum mechanics and general relativity. Unlike previous approaches that struggle with mathematical consistency or experimental testability, our framework provides: (1) a precise scale-dependent product that smoothly interpolatesopenaire +1 more source
This paper, the fourth in a series, culminates the development of a novel paradigm termed **Transdimensional Mathematics**. This framework unifies continuous and discrete mathematical structures through the fundamental interaction of positive and negative spatial dimensions, with core relations such as $xX = a = \text{const.}$ describing an ...
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C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics
The present book grew from lecture notes we have written for participants of lectures on applications of C^{∗}-algebra theory to the foundations of quantum statistical mechanics, as well as a mini-course on thermodynamic equilibrium of quantum lattice systems with mean-field interactions, we held at the Institute of Physics of the University of São ...Bru, J.-B., de Siqueira Pedra, W.
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C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics
2023Jean-Bernard Bru +1 more
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2017
This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory ...
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This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory ...
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This work presents a unified hyperdimensional scientific framework — Tetrahedral Hypergeometry — which models all known phenomena, from quantum mechanics to consciousness, as recursive morphogenetic flows of Clifford-phase structures. Building on classical mathematics, modern physics, and visionary extensions, we propose that reality is a living ...
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The core axiom of this framework is that the vacuum has a finite structural capacity for energy density (derived from the Planck limit). Interactions are modeled not as linear superposition, but as non-linear saturation events using the rule: -phi (x) -phi -> P_max.
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