Polar analysis of the Dirac equation through dimensions
DIME Sez. Metodi e Modelli Matematici, Università di Genova, Via all’Opera Pia 15, 16145, Genova, Italy
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Accepted: 23 March 2019
Published online: 30 April 2019
We consider the polar form of the spinor field equation in an n -dimensional space-time, studying the way in which the space-time dimension influences the number of the independent field equations and the number of the degrees of freedom of the spinor field written in the polar form: we will find that this polar form is the clearest tool to make manifest the fact that the degrees of freedom of the spinor field and the independent field equations match in dimensions 4 and 8 alone while in all the other instances there will be problems of general under-determination or over-determination.
© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019