On symmetry and topological origin of Weyl particles
Abstract
We suggest that the Weil spinors originate from the multi  component fermion fields. Those fields belong to the unusual theory that, presumably, exists at extremely high energies. In this theory there is no Lorentz symmetry. Moreover, complex numbers are not used in the description of its dynamics. Namely, the one  particle wave functions are real  valued, the functional integral that describes the second  quantised theory does not contain the imaginary unit as well. In the low energy effective theory the two  component Weil spinors appear. Their appearance is related to the AtiyahBottShapiro construction and to the expansion of the real matrix near the topologically protected nodes in three dimensional momentum space. The complex numbers entering ordinary quantum mechanics emerge together with the Weil fermions. In this pattern gauge fields and gravitational fields appear as certain collective excitations (of the original theory) experienced by the low  energy Weil fermions.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 DOI:
 10.48550/arXiv.1312.1267
 arXiv:
 arXiv:1312.1267
 Bibcode:
 2013arXiv1312.1267V
 Keywords:

 Physics  General Physics
 EPrint:
 Latex, 12 pages