Course curriculum

  • 1

    Welcome to the course

    • Course requirement

    • Outline

    • Lecture Notes

    • lecture notes for beyond part

    • Textbook recommended by Amalia

    • Zoom links

    • Hadrons, color, eight fold way and all that

    • associated tutorial

    • associated tutorial solution

    • CPT symmetric universe and neutrino dark matter

  • 2

    Introduction: motivation, outline and mathematical preliminaries

    • Motivation and outline

    • Vector space and algebra with examples

    • More examples on algebra and groups

    • Group classification

    • Vector space and algebra with examples

    • Entertainment: poem reading

  • 3

    Gauge theory, Yang Mills theory

    • U(1) gauge theory

    • Non abelian gauge theory

    • Tutorial one

    • Entertainment: poem reading 2

    • Tutorial one solution

  • 4

    Standard model in a nutshell

    • How to build a gauge theory

    • Standard Model as a gauge theory

    • Entertainment joke

  • 5

    Lagrangian of Standard Model

    • Criteria and dimensional analysis

    • Kinetic term for gauge bosons

    • Kinetic term for scalar

    • Kinetic term for fermions

    • Recap and boson interaction term

    • Yukawa term

    • Yukawa continued

    • Tutorial Two

    • Tutorial two solution

    • The last bit

    • Tally the parameters

    • Status of the standard model

    • Entertainment physics poem

    • Entertainment poem by student

    • Entertainment poem reading 3

    • Homework One

  • 6

    Spontaneously symmetry breaking (Higgs Mechanism)

    • Higgs VEV

    • Vacuum manifold

    • Goldstone boson

    • Eaten goldstone boson

    • SSB in standard model: boson sector

    • SSB in standard model: massive vector bosons

    • General case

    • SSB in standard model fermion sector

    • SSB standard model fermion mass

    • Undiagonalized weak interaction

    • Poem by student 2

    • Poem by another student

    • Entertainment ode to joy with bare hands

    • Tutorial three

    • Tutorial three solution

  • 7

    Interactions and their Feynman diagrams

    • Sample Feynman rules

    • Interaction gauge boson

    • Interaction Higgs

    • Interaction fermions

    • Entertainment poem and a few beginning of poems

    • Tutorial Four

    • Tutorial four solution

    • SMB_hw2

    • Discussion on Standard Model and its problems, Higgs potential with temperature, RG flow of Higgs potential

  • 8

    Neutrinos

    • A tale of three models

    • The Weinberg term

    • Majorana fermions

    • Two other symmetries

    • SMEFT cont

    • Lepton and baryon number

    • vSM

    • Equivalence to SMEFT

    • see saw mechanism

    • see saw cont

    • dark matter

    • Tutorial and hw 3

    • SMBtut52021solution_neutrino

  • 9

    Anomalies

    • Standard Model recap

    • Motivation

    • Global and gauge anoamlies

    • global anomalies: simplest example

    • global anomalies: apply to the standard model

    • gauge anomalie: one example

    • gauge anomalies: more examples

    • two exercises (we will do in tutorial)

    • Tutorial Six: anomalie

    • Tutorial Six solution

  • 10

    Grand Unification Theories (GUT)

    • Re Represent the table

    • Introduction to 3 GUTs

    • Embedding in SU(5)

    • Exterior algebra

    • property of exterior algebra

    • exterior algebra and standard model particles

    • SO(10) unification

    • pros and cons of SU(5) v.s. SO(10)

    • Pati-Salam unification

    • question about unification

    • Effectie field theory (EFT) and Renormalization group (RG)

    • Answers given by GUT: unified gauge couplings

    • Bad news

    • good news from SUSY and inflation

    • bad news again

    • SMB_2021_GUT

    • SMB_GUT_solution_2021

  • 11

    The magic square and the standard model

    • Read the following lecture notes, most of it should be a review. The video lecture was the first in pandemic and was not recorded.

    • Jordan algebras

    • symmetry: automorphism and derivation

    • Jordan derivation

    • question about Jspin and H2(O)

    • three main algebras

    • derivation algebra of Hn(K)

    • tutorial 8: octonion

    • tutorial 8 solution

    • projective plane

    • magic square construction

    • References and triality

    • standard model gauge group emerges

    • geometry interpretation

    • bad news: what about spinors

    • fun observations about Dynkin diagrams

    • complex representations and three families

    • Latham's paper on this subject last June

    • Latham's talk on this subject with new material

    • end of course entertainment by Gang: nose flute

    • Tut 9: Magic square

    • Hint