On symmetry and topological origin of Weyl particles

TL;DR

This paper proposes that Weyl spinors originate from a high-energy, non-Lorentz-invariant theory with real-valued wave functions, where complex numbers and gauge fields emerge at low energies through topological and symmetry considerations.

Contribution

It introduces a novel high-energy framework where Weyl fermions and complex quantum mechanics emerge from real-valued fields without Lorentz symmetry.

Findings

Weyl spinors originate from real multi-component fermion fields.

Complex numbers and gauge fields emerge at low energies.

The theory relates topological features to the appearance 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 Atiyah-Bott-Shapiro 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.