## Course curriculum

• 1

### Welcome to the course

• Course requirement

• Outline

• Lecture Notes

• lecture notes for beyond part

• Textbook recommended by Amalia

• 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

• 3

### Gauge theory, Yang Mills theory

• U(1) gauge theory

• Non abelian gauge theory

• Tutorial one

• 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

• 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

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

• Answers given by GUT: unified gauge couplings

• good news from SUSY and inflation

• 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

• 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