物理・第43回NITEP談話会

Tuesday 23 Apr 2024, 13:30 → 17:30 Asia/Tokyo

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講師: Francesco Toppan (Centro Brasileiro de Pesquisas Físicas (CBPF), ブラジル)
題目：Mixed-brackets “metasymmetry” of braided Majorana qubits
日時：2024 年 4 月 23 日（火）13:30 〜 14:30
概要：The concept of “metasymmetry” which does not respect the even/odd grading of Lie superalgebras was introduced in 1990 by Leites and Serganova in the context of the so- called Volichenko algebras. Metasymmetry can play a role in parastatistics defined by mixed brackets which interpolate between ordinary commutators and anticommutators. The braidings of multiparticle Majorana qubits depend on an integer n = 2,3,4,.... For n = 2 one recovers ordinary fermions; for n > 2 a parastatistics where at most n − 1 paraparticles can be accommodated in a given sector; in the n → ∞ limit one recovers the spectrum of an ordinary bosonic theory. In this talk I introduce the notion of “generalized mixed-brackets Heisenberg-Lie algebras”, labeled by the integer n. It is shown that they act as dynamical metasymmetries of the multiparticle braided Majorana qubits for the corresponding value of n.

講師: Shintaro Yamamoto (Tokyo University of Science, Noda)
題目：Spectral flow of fermions in the CP2 (anti-)instanton, and the sphaleron with van- ishing topological charge
日時：2024 年 4 月 23 日（火）14:40 〜 15:20
概要：The spectral flow is ubiquitous in the physics of soliton-fermion interacting systems. Due to the effect of the topology of such systems, fermion zero modes (or spectral flows) arise and the fermion densities are localized. We study the spectral flows related to a continuous deformation of background soliton solutions, which enable us to develop new insights into the emergence of fermionic zero modes and the localization mechanism of fermion densities. In this talk, we first introduce a class known as the texture type of topological solitons and see that the concept of spectral flow naturally appears through the deformation degree of freedom of the solitons. As an illustrative example, we inves- tigate a CP2 nonlinear sigma model in which there are the (anti-)instantons and also the sphalerons with vanishing topological charge. The standard Yukawa coupling of the fermion successfully generates infinite towers of the spectra and the spectral flow is ob- served as increasing size of such solitons. Within a certain range of the size, the localization of the fermions on the solitons appears. The avoided crossings occur at multiple points in the exchange of the flows, indicating a manifestation of the fermion exchange of the localizing aspect.

講師: Zhanna Kuznetsova (UFABC, S ̃ao Paulo)
題目：Minimal Z2 ×Z2-graded Lie algebras and superalgebras and related physical systems
日時：2024 年 4 月 23 日（火）15:30 〜 16:30
概要：The Lie algebraic structures graded by Z2 × Z2 finite group are split in two classes: (1) Z2 × Z2-graded Lie algebras and (2) Z2 × Z2-graded Lie superalgebras. Z2 × Z2-graded Lie algebras’ generators contain ordinary bosonic operators in (00) sector and exotic bosons in (01), (10) and (11) sectors. In Z2 ×Z2-graded Lie superalgebras we have bosonic operators in (00) sector, exotic bosons in (11) sector and so called pseudo-fermions in (01) and (10) sectors.

In the first part of the talk I present a classification of minimal Z2 × Z2-graded Lie algebras and Lie superalgebras mentioning their relation to some known supersymmetric systems.

In the second part of the talk I describe two physical models related to Z2 ×Z2-graded Lie algebra A1 from the classification. The first model is based on the introduction of a “bosonic superfield”. The second one is based on the graded group manifold method in “bosonic superspace”.