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Pré-Publication, Document De Travail Année : 2022

Quantum mechanics with only real numbers

Résumé

We show that every Clifford algebra can be transformed into a formalism that uses only real numbers. The rules we must follow to achieve this are universal. To illustrate the method we construct the real pendant of SU(2) and we derive a version of the Dirac equation that uses only real numbers. The advantage of the complex formulations is that they reduce the size of the representation matrices by a factor of 2. The reason for the presence of complex numbers in quantum mechanics is that it is formulated in the language of group representation theory.

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Dates et versions

hal-03559591 , version 1 (07-02-2022)
hal-03559591 , version 2 (11-02-2022)

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  • HAL Id : hal-03559591 , version 2

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Gerrit Coddens. Quantum mechanics with only real numbers. 2022. ⟨hal-03559591v2⟩
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