Expressions of algebra elements and transcendental noncommutative calculus

Details Expressions of algebra elements and transcendental noncommutative calculus Expressions of algebra elements and transcendental noncommutative calculus

2007-11-16

arxiv.org/abs/0711.2608v2

Noncommutative Geometry and Physics 2005, Proceedings of the International Sendai-Beijing Joint Workshop, (2007)

Mathematics

Quantum Algebra

Scientific paper

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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