JETP Letters

, Volume 99, Issue 8, pp 481–486 | Cite as

Emergent Weyl fermions and the origin of i = \(\sqrt { - 1} \) in quantum mechanics

  • G. E. Volovik
  • M. A. Zubkov


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 multicomponent 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.


Higgs Boson JETP Letter Gauge Field Dirac Point Majorana Fermion 
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Copyright information

© Pleiades Publishing, Inc. 2014

Authors and Affiliations

  1. 1.Lounasmaa LaboratoryAalto University, School of Science and TechnologyAaltoFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Alikhanov Institute for Theoretical and Experimental PhysicsMoscowRussia
  4. 4.Department of Applied MathematicsThe University of Western OntarioLondonCanada

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