2011

Division Algebras and Quantum Theory

Baez, John C.

Understand

Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions.

Indeed, these three choices appear naturally in a number of axiomatic approaches.
However, there are internal problems with real or quaternionic quantum theory.
Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure.

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