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Quantum Register Algebra: the mathematical language for quantum computing
Quantum Information Processing, 2023 11 ...
Jaroslav Hrdina +7 more
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Algebraic quantum codes: linking quantum mechanics and discrete mathematics [PDF]
International Journal of Computer Mathematics: Computer Systems Theory, 2020 19 pages; written for both mathematicians and ...
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Hypercomplex Algebras and their application to the mathematical formulation of Quantum Theory
, 2014 Quantum theory (QT), namely in terms of Schrödinger's 1926 wave functions in general requires complex numbers to be formulated. However, it soon turned out to even require some hypercomplex algebra. Incorporating Special Relativity leads to an equation (Dirac 1928) requiring pairwise anti-commuting coefficients, usually $4\times 4$ matrices.
Hertig, Torsten +2 more
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Quantum gravity observables: observation, algebras, and mathematical structure*
Journal of Physics A: Mathematical and TheoreticalAbstract The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables (gravitationally dressed, field relational, and more general) is outlined.
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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 interpolates
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This monograph presents a complete, self-contained extension of Operational Mathematics– the theory of extending the repetition count of basic mathematical operations (addition,multiplication, exponentiation, tetration, and higher hyperoperations) from natural numbers to integers, rational numbers, real numbers, and complex numbers– to the setting of ...
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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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This paper proposes a new approach to describing fundamental interactions, based on the concept of an information quantum – an indivisible entity whose sole property is an integer information charge. An information interaction operation a∘ba∘b is introduced, which is non-commutative and describes three fundamentally different types of processes ...
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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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Book Review: Lie Algebras and Quantum Mechanics and Vector Bundles in Mathematical Physics [PDF]
Bulletin of the American Mathematical Society, 1973 P. R. Chernoff, J. E. Marsden
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