## Research |

Condensed matter systems with emergent relativistic invariance may serve as an arena for the experimental observation of various effects typical for the high - energy physics. In particular, some of such effects were predicted and checked experimentally in 2+1 D graphene, where the relativistic 2+1 D fermions appear in the vicinity of the Fermi points (see the detailed review in
In the previous papers the Anomalous Quantum Hall Effect (AQHE) was considered within the lattice regularized quantum field theory and within the tight - binding models of the solid state physics. The expression for the Hall current (through the topological invariant in momentum space N
Study of momentum space topology was initiated within the condensed matter physics (see the mentioned above monograph by G.E.Volovik). In particular, the momentum space topological invariants protect gapless fermions on the boundaries of topological insulators. Topological invariants in momentum space protect also the bulk gapless fermions in Dirac and Weyl semimetals. The large variety of topological defects and textures exist in the fermionic superfluids, and the gapless fermions associated with these objects are described by momentum space topology. Momentum space topology was also discussed in the context of relativistic quantum field theory (QFT). In my previous works the topological invariants in momentum space have been considered for the lattice regularization of QFT with Wilson fermions. Appearance of the massless fermions at the intermediate values of bare mass parameter was related to the jump of the introduced momentum space topological invariant. This invariant may actually be used for the description of a certain class of topological insulators. Also I studied the model with overlap fermions on the same grounds. In particular, the possible physical meaning of the zeros of the Green function has been discussed. The momentum space topological invariants are expressed in terms of the Green functions. Therefore, they are applicable both to the non - interacting and to the interacting systems. Suppose, that we start from the model without interactions. When the interactions are turned on, the value of the topological invariant is not changed until the phase transition is encountered. This means, that the properties of the system described by the given topological invariant are robust to the introduction of interactions. The more simple non - interacting model may be investigated in order to describe such properties of the complicated interacting system.
The idea, that the 125 GeV Higgs boson of the SM may be composed of fermions follows the analogy with the models of superconductivity and superfluidity. Historically, first it was suggested, that Higgs boson is composed of additional technifermions. This theory contains an additional set of fermions that interact with the Technicolor (TC) gauge bosons. This interaction is attractive and, therefore, by analogy with BCS superconductor theory it may lead to the formation of fermionic condensate. This condensate, in turn, breaks Electroweak symmetry down to Electromagnetism. It is worth mentioning that TC theory suffers from the problems related to fermion mass generation. Extended Technicolor (ETC) interactions do not pass precision Electroweak tests due to the flavor changing neutral currents and due to the contributions to the Electroweak polarization operators (S and T parameters). The so-called walking technicolor improves the situation essentially, but the ability to generate top quark mass remains problematical. It was suggested by V.A. Miransky and co - authors
2 G.E. Volovik, The Universe in a Helium Droplet, Clarendon Press, Oxford (2003); G.E. Volovik, “Analog of gravity in superfluid He3-A”, JETP Lett. 44, 498--501 (1986); P. Horava, “Stability of Fermi surfaces and K-theory”, Phys. Rev. Lett. 95, 016405 (2005) 3 O.Chandia and J.Zanelli, ``Topological invariants, instantons and chiral anomaly on spaces with torsion,'' Phys. Rev.D 55 (1997) 7580 [hep-th/9702025]; E.W.Mielke, ``Anomalies and gravity,'' AIP Conf.Proc. 857B (2006) 246 [hep-th/0605159]; D.Kreimer and E.W.Mielke, ``Comment on: Topological invariants, instantons, and the chiral anomaly on spaces with torsion,'' Phys. Rev. D 63 (2001) 048501 [gr-qc/9904071]; Onkar Parrikar, Taylor L. Hughes, Robert G. Leigh, Phys. Rev. D 90, 105004 (2014), arXiv:1407.7043 4 M. A. Stephanov and Y. Yin, “Chiral Kinetic Theory,” Phys. Rev. Lett. 5 V.A. Miransky, Masaharu Tanabashi, and Koichi Yamawaki, “Is the t quark responsible for the mass of W and Z bosons?" Mod. Phys. Lett. A 4, 1043-1053 (1989) 6 H.Terazawa, Y.Chicashige, K.Akama, Phys. Rev. D 15, 480 (1977) |

עדכון אחרון ב-רביעי, 21 פברואר 2018 13:21 |