WSB04000 Lattice Quantum Chromodynamics

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Physics Program

Lecture Code WSB04000 Subject Classification Specialized Education

Subject Name 格子量子色力学

Subject Name
（Katakana）コウシリョウシイロリキガク

Subject Name in
English Lattice Quantum Chromodynamics

Instructor ISHIKAWA KENICHI

Instructor
(Katakana) イシカワ　ケンイチ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  3Term

Days, Periods, and Classrooms (3T) Weds1-4：SCI A004

Lesson Style Lecture Lesson Style
(More Details) 　

use black boards and PC presentation.
Some reports and homeworks will be assigned.

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 6 : Graduate Advanced

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 06 : Physics

Eligible Students M1, M2

Keywords quantum mechanics, quantum field theory, special relativity,
Quantum Chromodynamics (QCD), elementary particles, lattice gauge theory.

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)

Class Objectives
/Class Outline The interactions among elementary particles are all described by gauge theories based on the gauge invariance principle. There are various methods to analyze the gauge interactions to understand the matter behavior. Analytic perturbation methods have been used for electromagnetic, weak, and strong interactions at high energy region.  However the analytic method fails for the strong interaction in low energy since the strength of the interaction does not permit the perturbative analysis. The lattice field theory, which is a numerical non-perturbative method, is suitable for such a strongly interacting theory.

In this lecture I will give a series of introductory lecture for the lattice quantum Chromodynamics(QCD).
QCD is the theory describing the interaction among nuclei and  difficult to analyze perturbatively.

Class Schedule lesson1
Review on quantum mechanics (Lagrangean and Hamitonian)
lesson2
Path-integral quantization I (Hamiltonian and time evolution operators)
lesson3
Path-integral quantization II (Path-integral rep.)
lesson4
Path-integral quantization III (relation between many particles and fields)
lesson5
Path-integral quantization IV (Euclidean theory and integration on many variables)
lesson6
Path-integral quantization V (relation to statistical mechanics/thermodynamics, and perturbation theory)
lesson7
Quantization of scalar fields (Klein-Gordon fields) on a lattice I (constructing actions in continuous space-time and in lattice space-time)
lesson8
Quantization of scalar fields on a lattice II (characteristics of propagators)
lesson9
Quantization of scalar fields on a lattice III (short introduction to perturbation theory)
lesson10
Gauge fields and gauge invariance/covariance I (the standard model of elementary particles, U(1) gauge theory in continuous space-time)
lesson11
Gauge fields and gauge invariance/covariance II (SU(N) gauge theory in continuous space-time)
lesson12
Quantization of gauge fields on a lattice I (Constructing gauge transformation and action on the lattice)
lesson13
Quantization of gauge fields on a lattice II (Integration measure on group manifold and path-integral of gauge field)
lesson14
Quantization of fermion fields on a lattice (fermion and chiral symmetory)
lesson15
Lattice Quantum Chromodynamics (Lattice QCD)

Reports and homeworks will be assigned.
No priodic exams.

Text/Reference
Books,etc. 大川正典、石川健一共著「格子場の理論入門」SGCライブラリ 140臨時別冊・数理科学サイエンス社 JAN 4910054700480
青木慎也著「格子上の場の理論」シュプリンガー現代理論物理学シリーズ, シュプリンガー・ジャパン.
Heinz J. Rothe 著, "Lattice Gauge Theories: An Introduction", (World Scientific Lecture Notes in Physics) World Scientific Pub Co Inc.
「ゲージ理論入門 I, II」I.J.R.エイチスン・A.J.G.ヘイ著，講談社サイエンティフィック.
“Quantum Fields on a Lattice”, ISTVAN MONTVAY and GERNOT MUNSTER, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press., ISBN 0-521-59917-2.

PC or AV used in
Class,etc. 　

(More Details) Black board and PC presentation

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review It is recommended to derive various equations given in the lectures by yourself.
"Lattice Gauge Theories: An Introduction" by H.J. Rothe is suitable for introductory self study.

Requirements

Grading Method Reports and homework (100%). A homework will be assigned every two classes based on the quarter system.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other We give lectures in English for students having not-enough Japanese language skills.

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Physics Program
Lecture Code	WSB04000	Subject Classification	Specialized Education
Subject Name	格子量子色力学
Subject Name （Katakana）	コウシリョウシイロリキガク
Subject Name in English	Lattice Quantum Chromodynamics
Instructor	ISHIKAWA KENICHI
Instructor (Katakana)	イシカワ　ケンイチ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Weds1-4：SCI A004
Lesson Style	Lecture	Lesson Style (More Details)
use black boards and PC presentation. Some reports and homeworks will be assigned.
Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	6 : Graduate Advanced
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	06 : Physics
Eligible Students	M1, M2
Keywords	quantum mechanics, quantum field theory, special relativity, Quantum Chromodynamics (QCD), elementary particles, lattice gauge theory.
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)
Class Objectives /Class Outline	The interactions among elementary particles are all described by gauge theories based on the gauge invariance principle. There are various methods to analyze the gauge interactions to understand the matter behavior. Analytic perturbation methods have been used for electromagnetic, weak, and strong interactions at high energy region. However the analytic method fails for the strong interaction in low energy since the strength of the interaction does not permit the perturbative analysis. The lattice field theory, which is a numerical non-perturbative method, is suitable for such a strongly interacting theory. In this lecture I will give a series of introductory lecture for the lattice quantum Chromodynamics(QCD). QCD is the theory describing the interaction among nuclei and difficult to analyze perturbatively.
Class Schedule	lesson1 Review on quantum mechanics (Lagrangean and Hamitonian) lesson2 Path-integral quantization I (Hamiltonian and time evolution operators) lesson3 Path-integral quantization II (Path-integral rep.) lesson4 Path-integral quantization III (relation between many particles and fields) lesson5 Path-integral quantization IV (Euclidean theory and integration on many variables) lesson6 Path-integral quantization V (relation to statistical mechanics/thermodynamics, and perturbation theory) lesson7 Quantization of scalar fields (Klein-Gordon fields) on a lattice I (constructing actions in continuous space-time and in lattice space-time) lesson8 Quantization of scalar fields on a lattice II (characteristics of propagators) lesson9 Quantization of scalar fields on a lattice III (short introduction to perturbation theory) lesson10 Gauge fields and gauge invariance/covariance I (the standard model of elementary particles, U(1) gauge theory in continuous space-time) lesson11 Gauge fields and gauge invariance/covariance II (SU(N) gauge theory in continuous space-time) lesson12 Quantization of gauge fields on a lattice I (Constructing gauge transformation and action on the lattice) lesson13 Quantization of gauge fields on a lattice II (Integration measure on group manifold and path-integral of gauge field) lesson14 Quantization of fermion fields on a lattice (fermion and chiral symmetory) lesson15 Lattice Quantum Chromodynamics (Lattice QCD) Reports and homeworks will be assigned. No priodic exams.
Text/Reference Books,etc.	大川正典、石川健一共著「格子場の理論入門」SGCライブラリ 140臨時別冊・数理科学サイエンス社 JAN 4910054700480 青木慎也著「格子上の場の理論」シュプリンガー現代理論物理学シリーズ, シュプリンガー・ジャパン. Heinz J. Rothe 著, "Lattice Gauge Theories: An Introduction", (World Scientific Lecture Notes in Physics) World Scientific Pub Co Inc. 「ゲージ理論入門 I, II」I.J.R.エイチスン・A.J.G.ヘイ著，講談社サイエンティフィック. “Quantum Fields on a Lattice”, ISTVAN MONTVAY and GERNOT MUNSTER, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press., ISBN 0-521-59917-2.
PC or AV used in Class,etc.
(More Details)	Black board and PC presentation
Learning techniques to be incorporated
Suggestions on Preparation and Review	It is recommended to derive various equations given in the lectures by yourself. "Lattice Gauge Theories: An Introduction" by H.J. Rothe is suitable for introductory self study.
Requirements
Grading Method	Reports and homework (100%). A homework will be assigned every two classes based on the quarter system.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other	We give lectures in English for students having not-enough Japanese language skills.
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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