Author(s)

Doron Kwiat

Independent Researcher, Mazkeret Batyia, Israel.

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 = 2^D 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.

Fermions, Dirac Equation, D-Dimensional Universe, N Dimensional Gamma Matrices, Irreducible Representations

Kwiat, D. (2022) D Dimensions and N × N Matrix Representations of Fermions. Journal of High Energy Physics, Gravitation and Cosmology, 8, 635-641. doi: 10.4236/jhepgc.2022.83045.