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arXiv · 0711.2608

Expressions of algebra elements and transcendental noncommutative calculus

Hideki Omori·Yoshiaki Maeda·Naoya Miyazaki·Akira Yoshioka
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Abstract

Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that $\frac{1}{i\h}uv$ in the Weyl algebra is naturally viewed as an indeterminate living in a discrete set $\mathbb{N}{+}{1/2}$ {\it or} ${-}(\mathbb{N}{+}{1/2})$ . This may yield a more mathematical understanding of Dirac's positron theory.

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Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka. 2007-11-23. Expressions of algebra elements and transcendental noncommutative calculus. https://doi.org/10.1142/9789812779649_0001

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