Osaka Univ. Particle Physics Theory Group
Intensive Lectures

特別講義　AI
くりこみ群と自発的質量生成

講師

青木　健一 (金沢大学理工研究域)

日時

Dec 17(10:30--),18(10:30--) Seminar at H711 (15:30--),19(9:30--)

場所

E210

授業の目的

Renormalization group is a method applied to various areas in physics, since it consists of very basic and common notions of dimensional analysis, coarse graining, effective theory and scaling behaviors. This course will calarify these fundamental features of renormalization group method by using very simple model systems, and also by applying it to the spontaneous mass generation problems in gauge theories.

履修条件・受講条件

No special knowledges are required except for fundamentals in quantum mechanics, and in the latter part of the course, basics and the perturbation theory in field theory.

講義内容

Central ingredients of renormalization group method will be explained by using simple probabilistic processes, random walks. Application to the statistical mechanics is formulated with Ising models and notions of phase transition and spontaneous symmetry breaking are introduced. Then the spontaneous mass generation in gauge theories will be investigated by renormalization group as a field theoretical realization of the spontaneous symmetry breaking and the chiral phase transition, including finite temperature and finite density cases.

授業計画

1. Introduction and historical background -- Path integral and statistical mechanics

2. Probabilistic processes, random walks -- Coarse graining and renormalization group

3. Statistical mechanics, Ising models -- Phase transition and spontaneous symmetry breaking

4. Field theory, QCD in finite temperature and finite density -- Spontaneous mass generation in gauge theories

教科書

No textbooks are assigned to this course.

参考文献

Introduction to the Non-perturbative Renormalization Group and Its Recent Applications, K-I.Aoki, Int. J. Mod. Phys. B14 (2000) 1249--1326

コメント

No knowledge is required to understand the essential formulation and its power of renormalization group method. It means that renormalization group should have many new application in wider fields of science (at least described by mathematics), and students are hoped to find one some day in the future.

特別講義　AII
超弦理論のダイナミクスと非摂動的定式化

講師

川合 光 (京都大学大学院理学研究科)

日時

Dec 3 (13:00~),4(10:30~),5(10:30~)

場所

E210

授業の目的

弦理論とその非摂動的定式化について学ぶ。

履修条件・受講条件

-

講義内容

超弦理論は重力も含めて、すべての力と物質を統一的に記述 する有力な候補である。しかしながら、そのダイナミクスは 完全には理解されておらず、基底状態（真空）がどのような メカニズムで決定されているか、また、どれくらい多くの真 空が存在するかなど、未知の点も多い。 超弦理論のダイナミクスを理解するためには、摂動論に依存 しない定式化（非摂動的定式化）が必要であるが、その可能 性の一つである行列模型を中心として、今後の超弦理論の進 むべき方向性について議論したい。

授業計画

-

教科書

特になし。

参考文献

講義中に適宜紹介する。

コメント

-