Transcription of Lecture Notes on Quantum Field Theory
1 Draft for Internal Circulations:v1: Spring Semester, 2012, v2: Spring Semester, 2013v3: Spring Semester, 2014, v4: Spring Semester, 2015 Lecture Notes on Quantum Field TheoryYong Zhang1 School of Physics and Technology, Wuhan University, China(Spring 2015)AbstractThese lectures Notes are written for both third-year undergraduate studentsand first-year graduate students in the School of Physics and Technology,University Wuhan, China. They are mainly based on Lecture Notes of SidneyColeman from Harvard and Lecture Notes of Michael Luke from Toronto andlecture Notes of David Tong from Cambridge and the standard textbook ofPeskin & Schroeder, so I do not claim any originality.
2 These Notes certainlyhave all kinds of typos or errors, so they will be updated from time to time. Ido take the full responsibility for all kinds of typos or errors (besides errors inEnglish writing), and please let me know of third version of these Notes are typeset by a team including:Kun Zhang2, Graduate student (Id: 2013202020002),Participant in the Spring semester, 2012 and 2014Yu-Jiang Bi3, Graduate student (Id: 2013202020004),Participant in the Spring semester, 2012 and 2014 The fourth version of these Notes are typeset byKun Zhang, Graduate student (Id: 2013202020002),Participant in the Spring semester, 2012 and for Internal Circulations:v1: Spring Semester, 2012, v2: Spring Semester, 2013v3: Spring Semester, 2014, v4.
3 Spring Semester, 2015 AcknowledgementsI thank all participants in class including advanced undergraduate students,first-year graduate students and French students for their patience and persis-tence and for their various enlightening questions. I especially thank studentswho are willing to devote their precious time to the typewriting of these lecturenotes in References to Lecture Notes * [Luke] Michael Luke (Toronto): online Lecture Notes on QFT (Fall, 2012);the link to Luke s homepage* [Tong] David Tong (Cambridge): online Lecture Notes on QFT (October 2012);the link to Tong s homepage* [Coleman] Sidney Coleman (Harvard): online Lecture Notes ;the link to Coleman s Lecture link to Coleman s teaching videos;* [PS] Michael E.
4 Peskin and Daniel V. Schroeder:An Introduction to Quantum Field Theory , 1995 Westview Press;* [MS] Franz Mandl and Graham Shaw: Quantum Field Theory (Second Edition), 2010 John Wiley & Sons, Ltd.* [Zhou] Bang-Rong Zhou (Chinese Academy of Sciences): Quantum Field Theory (in Chinese), 2007 Higher Education Press;Main References to Homeworks* Luke s Problem Sets #1-6 or Tong s Problem Sets # Projects* See Yong Zhang s English and Chinese our parents and our teachers!To be the best researcher is to be the best person first of all:Respect and listen to our parents and our teachers always!3 Quantum Field Theory (I) focuses on Feynman diagrams and basic aim of this course is to study the simulation of both Quantum Field theoryand Quantum gravity on Quantum Quantum Field Theory (I): Basic Concepts and Feynman Diagrams 111 Overview of Quantum Field Definition of Quantum Field Theory .
5 Introduction to particle physics and Feynman diagrams .. diagrams in the pseudo-nucleon meson interaction .. diagrams in the Yukawa interaction .. diagrams in Quantum electrodynamics .. The canonical quantization procedure .. Research projects in this course .. 222 From Classical Mechanics to Quantum Classical particle mechanics .. formulation of classical particle mechanics .. formulation of classical particle mechanics .. s theorem: symmetries and conservation laws .. solved problems .. Theory .. Theory .. talk about classical particle mechanics in detail.
6 Advanced Quantum mechanics .. canonical quantization procedure .. principles of Quantum mechanics .. Schr oedinger, Heisenberg and Dirac picture .. Quantum many-body mechanics .. observable .. Heisenberg uncertainty principle .. and conservation laws .. solved problems in Quantum mechanics .. harmonic oscillator .. Time-independent perturbation Theory .. Time-dependent perturbation Theory .. Angular momentum and spin .. Identical particles .. Scattering Theory in Quantum mechanics .. 4053 Classical Field Special relativity .. transformation .. calculation.
7 Relation .. group .. of particles .. Classical Field Theory .. of fields .. fields .. , Hamiltonian and the action principle .. simple string Theory .. scalar Field Theory .. scalar Field Theory .. scalar Field Theory .. relativity .. 544 Symmetries and Conservation Symmetries play a crucial role in Field theories .. Noether s theorem in Field Theory .. Space-time symmetries and conservation laws .. translation invariance and energy-momentum tensor .. transformation invariance and angular-momentum tensor .. Internal symmetries and conservation laws.
8 S theorem .. (2) invariant real scalar Field Theory .. (1) invariant complex scalar Field Theory .. internal symmetries .. Discrete symmetries .. reversal .. conjugation .. 705 Constructing Quantum Scalar Field Quantum mechanics and special relativity .. units .. number unfixed at high energy (Special relativity) .. position operator at short distance ( Quantum mechanics) .. and algebra of local observables .. naive relativistic single particle Quantum mechanics .. Comparisons of Quantum mechanics with Quantum Field Theory .. Definition of Fock space .. Rotation invariant Fock space.
9 Space .. number representation (ONR) .. from simple harmonic oscillator (SHO) .. operator formalism of Fock space in a cubic box .. the box normalization and take the continuum limit .. Lorentz invariant Fock space .. group .. of Lorentz invariant normalized states .. invariant normalized state .. Constructing Quantum scalar Field Theory .. Quantum scalar Field .. Canonical quantization of classical Field Theory .. Field Theory .. quantization .. energy, Casimir force and cosmological constant problem .. ordered product .. Symmetries and conservation laws.
10 (2) invariant Quantum real scalar Field Theory .. (1) invariant Quantum complex scalar Field Theory .. symmetries .. reversal .. conjugation .. CPT theorem .. Micro-causality (Locality) .. scalar Field Theory .. scalar Field Theory .. Remarks on canonical quantization .. 1016 Feynman Propagator, Wick s Theorem and Dyson s Retarded Green function .. scalar Field Theory with a classical source .. retarded Green function .. formulation ofDR(x y) .. quantization of a real scalar Field Theory with a classicalsource .. Advanced Green function .. The Feynman PropagatorDF(x y).
