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Majorana fermions in condensed-matter physics. (English) Zbl 1347.81074

Summary: It is an honor and a pleasure to have been invited to give a talk in this conference celebrating the memory of the late Professor Abdus Salam. To my regret, I did not know Professor Salam personally, but I am very aware of his work and of his impact on my area of specialization, condensed matter physics, both intellectually through his ideas on spontaneously broken symmetry and more practically through his foundation of the ICTP. Since I assume that most of this audience are not specialized in condensed-matter physics, I thought I would talk about one topic which to some extent bridges this field and the particle-physics interests of Salam, namely Majorana fermions (M.F.s). However, as we shall see, the parallels which are often drawn in the current literature may be a bit too simplistic. I will devote most of this talk to a stripped-down exposition of the current orthodoxy concerning M.F.s. in condensed-matter physics and their possible applications to topological quantum computing (TQC), and then at the end briefly indicate why I believe this orthodoxy may be seriously misleading.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81P68 Quantum computation
81T45 Topological field theories in quantum mechanics
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
20B30 Symmetric groups
82D20 Statistical mechanics of solids
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References:

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