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)

PatiSalam 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
