Emergent Weyl fermions and the origin of

in quantum mechanics

G. E. Volovik^{+*}, M. A. Zubkov ^{×}

^{+}Lounasmaa Laboratory, Aalto University, School of Science and Technology, FI-00076 AALTO, Finland

^{*}Landau Institute for Theoretical Physics of the RAS, 119334 Moscow, Russia

^{×}Alikhanov Institute for Theoretical and Experimental Physics, 117259 Moscow, Russia

^{°}Department of Applied Mathematics, The University of Western Ontario, N6A 5B7 London (ON), Canada

**Abstract**

Conventional quantum mechanics is described in terms of complex numbers.
However, all physical quantities are real. This indicates, that the appearance
of complex numbers in quantum mechanics may be the emergent phenomenon, i.e.
complex numbers appear in the low energy description of the underlined high
energy theory. We suggest a possible explanation of how this may occur. Namely,
we consider the system of multi-component Majorana fermions. There is a
natural description of this system in terms of real numbers only. In the
vicinity of the topologically protected Fermi point this system is described by
the effective low energy theory with Weyl fermions. These Weyl fermions interact
with the emergent gauge field and the emergent gravitational field.