| 授業の目的 【日本語】 | | Theme: Quantum algebras and their representations
Quantum physics has been an exciting discipline which is so powerful and at the same time mysterious.
There have been plenty of mathematical endeavor to understand it.
Superficially it seems successful enough but the mathematical soundness is still incomplete.
It is in fact a big challenge to fill any gap remaining there and this is a first and final course to try to overcome its difficulties.
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| 授業の目的 【英語】 | | |
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| 到達目標 【日本語】 | | To get an acquaintance with the volunteering research attitudes and have a critical view points on such a stupid(silly) requirement to fill up formalities like this.
It is a basic skill to achieve any meaningful results and needs talented abilities to criticize meaningless performances.
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| 到達目標 【英語】 | | |
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| 授業の内容や構成 | | It depends on skills of participants but a rough subject order in the seminar is the following:
*-algebras and *-representations,
Gelfand theory,
Positivity in C*-algebras,
*representations and von Neumann algebras,
Order continuity in von Neumann algebras,
Tomita-Takesaki theory,
The standard form of von Neumann algebras,
Automorphic actions and KMS states,
Direct integrals and disintegration,
Canonical quantum algebras,
Clifford algebras,
Weyl algebras
Quantum states and their representations |
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| 履修条件 | | All the basics of undergraduate courses in math, especially including functional analysis and basic algebraic systems such
as group and ring in relations of linear algebra.
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| 関連する科目 | | | All the courses (though mostly in Japanese) provided in the Math department. |
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| 成績評価の方法と基準 | | Based on weekly reports in an oral or written form, which evaluates the degree of understanding the subject as well as presentability.
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| 教科書・テキスト | | Free states on CCR algebras
http://www.math.nagoya-u.ac.jp/~yamagami/teaching/lecture2014.pdf |
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| 参考書 | | Operator algebras and their representations
http://www.math.nagoya-u.ac.jp/~yamagami/teaching/oarep2014.pdf |
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| 課外学習等（授業時間外学習の指示） | | |
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| 注意事項 | | |
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| 他学科聴講の可否 | | |
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| 他学科聴講の条件 | | Informal attendance is welcome if it does not violate the course order.
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| レベル | | |
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| キーワード | | | quantum algebra, free states, *-representations |
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| 履修の際のアドバイス | | | Don't wait for any instructions. |
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| 授業開講形態等 | | |
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| 遠隔授業（オンデマンド型）で行う場合の追加措置 | | |
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