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In this paper, the Quaternion-valued Hardy spaces and conjugate Hardyspaces on are characterized. In analogy with the decomposition of square-integrable function space on the real line into the direct sum of Hardy space and conjugate Hardy space, the square-integrable Quaternion -valued function...
Clifford algebraic geometry corresponds to Minkowski space. Using the discrete structure of Minkowski space, we can abstract a class n-dimensional hyperbolic Hilbert phase space. To discussing the causality of physical event in Minkowski space, we can obtain the geometrical interpretation of...
This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University of Fukui. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do full three dimensional “drawings” on the screen. The...
By using hyperbolic virtual unit of Clifford algebra, the concept of n -dimensional space-time unit spheres is introduced. It is used as n -dimensional Minkowski space-time and Lorentz transformation.
Quantum gravity has been so elusive because we have tried to approach it by two paths which can never meet: standard quantum field theory and general relativity. These contradict each other, not only in superdense regimes, but also in the vacuum, where the divergent zero-point energy would roll...
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born’s probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of probabilities which describe a kind of hyperbolic interference...
Self-dual 2–forms on play a fundamental role in gauge theory. For generalized Seiberg-Witten theory (and for some other purposes in mathematical physics) a notion of self-duality of 2–forms on is needed. There are several definitions, but the one given by (Bilge, Dereli, Koçak ; JMP 38(9),...
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