2013/12/04 by G. E. Volovik, M. A. Zubkov, Volovik, G. E. +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fermion #Gauge theory #General Physics (physics.gen-ph) #Geometry #Lorentz group #Lorentz transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Applications #Quantum mechanics #Spinor #Symmetry (geometry) #Theoretical physics #Topological Materials and Phenomena #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1312.1267
Latex, 12 pages
arxiv created 2013/12/04 · openalex publication_date 2013/12/04 · arxiv updated 2013/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.