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| VOLUME 113 (2021) | ISSUE 7 | PAGE 448 |
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Classification of emergent Weyl spinors in multi-fermion systems
M. A. Zubkov
Physics Department, Ariel University, 40700 Ariel, Israel National Research Center "Kurchatov Institute" - ITEP, 117259 Moscow, Russia
Abstract
In the fermionic systems with topologically stable Fermi points the emergent two-component Weyl fermions appear. We propose the topological classification of these fermions based on the two invariants composed of the two-component Green function. We define these invariants using Wigner-Weyl formalism also in case of essentially non-homogeneous systems. In the case when values of these invariants are minimal (  ) we deal with emergent relativistic symmetry. The
emergent gravity appears, and our classification of Weyl fermions gives
rise to the classification of vierbein. Transformations between emergent
relativistic Weyl fermions of different types correspond to parity
conjugation and charge conjugation.
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