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.
Domaines
Physique Quantique [quant-ph]
Origine : Fichiers produits par l'(les) auteur(s)