TITLE:
D Dimensions and N × N Matrix Representations of Fermions
AUTHORS:
Doron Kwiat
KEYWORDS:
Fermions, Dirac Equation, D-Dimensional Universe, N Dimensional Gamma Matrices, Irreducible Representations
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.8 No.3,
July
18,
2022
ABSTRACT: The connection between the number of dimensions and the size of the representation matrices in the Dirac equation has been discussed thoroughly and the restriction N2 = 2D was derived. In this summary, the result is brought again, this time with emphasis on the importance of irreducibility of the representations. As a counter example, the case of the neutrino is discussed where the above restriction does not hold, indicating that the Dirac equation, in this case, is reducible.