授業の目的 【日本語】
Goals of the Course(JPN) | | |
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授業の目的 【英語】
Goals of the Course | | Title : C*-algebraic methods in spectral theory
This course will provide an overview on some of the most recent tools introduced in functional analysis for the study of operators related to quantum mechanics. During the first lectures, we shall quickly review some basics properties of bounded and unbounded operators on Hilbert spaces, and introduce the spectral theorem for self-adjoint operators. After reviewing some definitions and properties related to C*-algebras, we shall show how crossed product C*-algebras are naturally linked to generalized Schroedinger operators, and how information on these operators can be deduced from representations of these algebras. A related construction involving twisted crossed product algebras and its application for magnetic systems will then be discussed. |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | |
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到達目標 【英語】
Objectives of the Course | | | Understand the constructions related to crossed product C*-algebras, and observe how this algebraic framework can be applied successfully to the spectral theory of operators. |
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授業の内容や構成
Course Content / Plan | | Content:
1: Linear operators on a Hilbert space
2: C*-algebras
3: Crossed product C*-algebras
4: Schroedinger operators and essential spectrum
5: Twisted crossed product C*-algebras
6: Pseudodifferential calculus
7: Magnetic systems |
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履修条件
Course Prerequisites | | | Knowledge on standard undergraduate linear algebra, calculus and advanced calculus. |
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関連する科目
Related Courses | | | Any courses on function spaces or on operator algebras. |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | Grades based on attendance and on written reports. An active participation of the students is expected. |
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教科書・テキスト
Textbook | | | Lecture notes will be provided for this course. |
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参考書
Reference Book | | W.O. Amrein, Hilbert space methods in quantum mechanics
G.B. Folland, A course in abstract harmonic analysis
G.J. Murphy, C*-algebras and operator theory
D.P. Williams, Crossed products of C*-algebras
More material will be available on
http://www.math.nagoya-u.ac.jp/~richard/Cstar.html |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | Students are supposed to read the notes between the lectures. The subjects of the reports can be chosen according to the interest of the students |
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注意事項
Notice for Students | | Additional information and material will be added regularly on
http://www.math.nagoya-u.ac.jp/~richard/Cstar.html |
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他学科聴講の可否
Propriety of Other department student's attendance | | |
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他学科聴講の条件
Conditions of Other department student's attendance | | | This course is open for any students at Nagoya University. Motivated undergraduate students are also welcome. |
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レベル
Level | | |
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キーワード
Keyword | | | Self-adjoint operators, spectrum, C*-algebras, C*-dynamical systems, crossed product, magnetic systems. |
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履修の際のアドバイス
Advice | | | It is certainly easier to attend a course in English and to discuss in this language in a quiet university environment rather than later in a busy life. |
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授業開講形態等
Lecture format, etc. | | | Hybrid, and online if necessary. Record of the lectures will be available on demand. |
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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
Additional measures for remote class (on-demand class) | | |
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