고급 양자역학

한양대학교
신상진

페이스북 트위터 카카오톡 네이버밴드 링크복사

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자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >물리학
강의학기

2014년 1학기

조회수

29,060

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차시별 강의

1.	Why Quantum Field Theory?	Relativistic Quantum Field Theory, Path Integral,
2.	Semi-classical Approximation and Perturbation Expansion	Stationary Integral and Perturbation Expansion, Classical Limit,
3.	Feynman Propagator and Scalar Exchange	Feynman Propagator, Scalar Exchange
	Why Electrons Push Each Other?	review of Scalar Exchange, Ve,ctor Exchange
4.	Spin and the Characters of Forces	Vector Exchange, Spin 2 Exchange, Inverse Square Law, Feynman Diagram
	Feynman Diagram	perturbative field theory, Feynman Rule,
5.	Feynman Rule and Symmetric Factor	Feynman Rule, Symmetric Factor
	Canonical Quantization / Noether Theorem	Canonical Quantization, Symmetry and Conservation Law
6.	Questions / Answers	Propagator D(x), Graviton polarization, Normal Ordering
	Energy-Momentum Tensor / Dirac Equation	Energy-Momentum Tensor, Dirac Equation
7.	Discrete Symmetries of Dirac Equation / Parity and change conjugation	Discrete Symmetries of Dirac Equation, Parity and change conjugation
	Time Reversal Symmetry and Kramer theorem / Lorentz transformation for Spinor	Time Reversal Symmetry and Kramer theorem, Lorentz transformation for Spinor
8.	Majorana Fermion	Majorana Fermion, Majorana mass
	Quantization of Dirac Field / Negative Frequency problem	Quantization of Dirac Field, How Negative Frequency problem can be solved by the second quantization
9.	Connection Between Spin - Statistic	Why spin half particles are fermions and spin one particles are bosons?
	Lorentz Transfotmation and Structure of Dirac Eq	We study how two Weyl spinors are connected by a parity. Why dirac spinors must be a 4 component. The answer is the parity invariance.
10.	Dirac Eq and Electon Magnetic Moment	Dirac Equation and Electon Magnetic Moment, We show g=2.
	Schwinger's correction to g=2 / Hubbard - Stratonovich Transformation	1. Schwinger's correction to g=2 ; 2. Hubbard - Stratonovich Transformation
11.	Spontaneous Symmetry breaking	Goldstone theorem: when continuous symmetry is broken spontaneously, massless particles appears. Coleman-Mermin-Wagner theorem: in one and 2 dimension, symmetry can not be broken and order is not possible.
	Quantum Effective Potential	Definition of Effective potential is given by Legendre transformation of connected potential W.
12.	Basic Renormalization Theory with Effective Potential	Calculation of Coleman-Weinberg potential and its renormalization will be explicitly demonstrated and thereby show how vacuum fluctuation can induce instability of old vacuum and sometimes lead to symmetry breaking.
13.	Magnetic Monopole / Non-abelian Gange Theory	We introduce the magnetic monopole and charge quantization as its consequence. We also introduce the non-abelian gauge theory and gauge prnciple.
	Anderson - Higgs Mechanism	Introduce the Higgs mechanism using the abelian Higgs model and then use it to explain how the gauge boson gets mass by eating goldstone boson.
14.	Superconductivity vs Superfluidity	We explain the superconductivity by abelian higgs model and show how the London quation can be obtained from it. Superfluidity is explained by the linearity of the dispersion relation which gives the lack of the density of state using Feynman argument.
	Symmetry Breaking and Instability by Quantum Fluctuation	We use the Weinberg-Coleman effective potential of fermion to explain the Peiels instability.
15.	Solitons : Kink, Vortex, Monopole	Starting from the kink, we introduce the various solitonic object in quantum field theory.
	Boson,Fermion and Anyon	We demonstrate the non-triviality of 360 degree rotation and the triviality of 720 degree rotation in 3 dimension, which lead to the possibility of fermion and boson as the only possibility in 3 dimension. On the other hand, there is no such triviality in two dimension, leading to anyon therein.