# Emergent Weyl spinors in multi-fermion systems

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**Emergent Weyl spinors in multi-fermion systems.** / Volovik, G.E.; Zubkov, M.A.

Research output: Contribution to journal › Article › Scientific › peer-review

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*NUCLEAR PHYSICS B*, vol. 881, pp. 514-538. https://doi.org/10.1016/j.nuclphysb.2014.02.018

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*NUCLEAR PHYSICS B*,

*881*, 514-538. https://doi.org/10.1016/j.nuclphysb.2014.02.018

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TY - JOUR

T1 - Emergent Weyl spinors in multi-fermion systems

AU - Volovik, G.E.

AU - Zubkov, M.A.

PY - 2014

Y1 - 2014

N2 - In Ref. [1] Hořava suggested, that the multi-fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions. The number of the components of these coarse-grained fermions is reduced compared to the original system. Here we consider the 3+13+1 D system and concentrate on the particular case when the Fermi surface has co-dimension p=3p=3, i.e. it represents the Fermi point in momentum space. First we demonstrate explicitly that in agreement with Hořava conjecture, in the vicinity of the Fermi point the original system is reduced to the model with two-component Weyl spinors. Next, we generalize the construction of Hořava to the situation, when the original 3+13+1 D theory contains multi-component Majorana spinors. In this case the system is also reduced to the model of the two-component Weyl fermions in the vicinity of the topologically stable Fermi point. Those fermions experience the emergent gauge field and the gravitational field given by the emergent vierbein. Both these fields (the emergent gauge field and the emergent gravitational field) originate from certain collective excitations of the original system. We speculate, that the given construction may be relevant for the high energy physics in the paradigm, in which the Lorentz symmetry as well as the gravitational and gauge fields are the emergent phenomena, i.e. they appear dynamically in the low energy approximation of the underlined high energy theory.

AB - In Ref. [1] Hořava suggested, that the multi-fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions. The number of the components of these coarse-grained fermions is reduced compared to the original system. Here we consider the 3+13+1 D system and concentrate on the particular case when the Fermi surface has co-dimension p=3p=3, i.e. it represents the Fermi point in momentum space. First we demonstrate explicitly that in agreement with Hořava conjecture, in the vicinity of the Fermi point the original system is reduced to the model with two-component Weyl spinors. Next, we generalize the construction of Hořava to the situation, when the original 3+13+1 D theory contains multi-component Majorana spinors. In this case the system is also reduced to the model of the two-component Weyl fermions in the vicinity of the topologically stable Fermi point. Those fermions experience the emergent gauge field and the gravitational field given by the emergent vierbein. Both these fields (the emergent gauge field and the emergent gravitational field) originate from certain collective excitations of the original system. We speculate, that the given construction may be relevant for the high energy physics in the paradigm, in which the Lorentz symmetry as well as the gravitational and gauge fields are the emergent phenomena, i.e. they appear dynamically in the low energy approximation of the underlined high energy theory.

U2 - 10.1016/j.nuclphysb.2014.02.018

DO - 10.1016/j.nuclphysb.2014.02.018

M3 - Article

VL - 881

SP - 514

EP - 538

JO - NUCLEAR PHYSICS B

JF - NUCLEAR PHYSICS B

SN - 0550-3213

ER -

ID: 849345