Pis’ma v ZhETF, vol. 105, iss. 4, pp. 245 – 246 2017 February 25 c Dirac and Weyl fermions: from Gor’kov equations to Standard Model (in memory of Lev Petrovich Gor’kov) G.E.Volovik1) Low Temperature Laboratory, Aalto University, School of Science and Technology, P.O. Box 15100, FI-00076 AALTO, Finland Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia P.N.Lebedev Physical Institute, RAS, 119991 Moscow, Russia Submitted 9 January 2017 DOI: 10.7868/S0370274X17040130 Application of quantum field theory to condensed matter physics began in Soviet Union around 1956– 1957 [1]. <...> In this approach the Fermi sea serves as an analog of the relativistic quantum vacuum – the Dirac sea. <...> The composite models developed by Nambu and Jona-Lasinio [3] and by Vaks and Larkin [4], where the Higgs bosons appear as a composite states of the fermion pairs, are the direct consequences of the Gor’kov theory. <...> In such models the original Weyl fermions of Standard Model (such as top quarks) play the role of the electrons in metals, while the composite Higgs bosons are analogs of the collective modes of the order parameter in superconductors [5, 6]. <...> Here we consider another consequence of theGor’kov theory of superconductivity, where the Weyl fermions emerge in superconductors as Bogoliubov quasiparticles. <...> This in particular takes place for superconductors of the symmetry class O(D2) [7–9], where the 4 left-handed and 4 right-handed topologically protected chiral fermions emerge, see Fig. 1. <...> Expansion of the Gor’kov Green’s function in the vicinity of each topologically protected Weyl point leads to the effective relativistic quantum field theory with effective gauge fields and the effective gravity. <...> This provides the hint for possible emergent origin of the “fundamental” Weyl fermions, gauge fields, and general relativity [10–12]. <...> The majority of the superconductivity classes discussed in Refs. [7–9] contain the topologically protected Weyl points and/or Dirac lines. <...> The systems withWeyl fermions should experience the effects related to chiral anomaly [20, 21] – production of the chiral charge in the external electric and magnetic fields, or in the effective gauge fields produced by deformations. <...> The points <...>