Theoretical Physics

Zhian Jia | 贾治安

Lecture Notes

"The best way to learn a new topic is to write a book about it." Paraphrase from Serge Lang， See "Serge Lang, 1927–2005".

This page will collect some of the lecture notes, tutorials, and expository articles that I write.

A list of lecture notes

Topological order, TQFT, Chern-Simons theory
CFT, RCFT
Quantum information, quantum computation
SPT, SET
IT FROM QUBIT
AdS/CFT, AdS/CMT

Tensor cateogory, Frobenius algebra
Vertex operator algebra
Functional analysis, operator algebra, convex analysis, finite geometry
Group cohomology, higher category

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2022

Quantum Information theory in a nutshell

Zhian Jia (2022, Jul, ver 0.0.2)

incomplete
PDF

Abstract

An incomplete lecture note on quantum information theory.

2020

Basic String Theory

Zhian Jia (2020, Sep.10 ver 0.0.1)

PDF

Abstract

A short introduction to string theory.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Quantum Information Theory

The modern field of quantum information theory contains numerous branches, including quantum foundations, quantum Shannon theory, various quantum protocols, and more. It also has overlapping connections with other areas of physics such as condensed matter physics, high energy physics, and quantum gravity.

Some general references

John Preskill, Course Information for Physics 219/Computer Science 219 Quantum Computation (Formerly Physics 229). This page is a collection of wonderful lecture notes by Preskill on quantum information theory. In Fall 2020 his course is recoded, see the online videos Ph/CS 219A Quantum Computation.

Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information. This a standard textbook for quantum information and quantum computation theory.

Mark Wilde, Quantum Information Theory. This book provides a comprehensive discussion of quantum Shannon theory, covering a wide range of topics in depth.

John Watrous, The Theory of Quantum Information. This is a book that contains many mathematical details on techniques used in quantum informtaion theory. His Theory of Quantum Information and Advanced topics in Quantum Information Theory are also very good reading materials.

Some useful numerical tools

QuTip, a python-based open-source software for simulating the dynamics of open quantum systems.

Quantum Information Theory

2020
Basic quantum information theory

Pdf version of notes. (incomplete, use at your risk).

Quantum inforamtion course: Page for QIT,
- 1. Quantum states as density operators: PDF
  Qubit and Bloch sphere; Density operator; Composed system and reduced states; Distance between quantum states; Entanglement I: pure state case; Entanglement II: mixed state case; Entanglement III: Bell inequality; Multipartite quantum state.
- 2. Measurement as positive operator-valued measure: PDF
  Qubit and Bloch sphere; Density operator; Composed system and reduced states; Distance between quantum states; Entanglement I: pure state case; Entanglement II: mixed state case; Entanglement III: Bell inequality; Multipartite quantum state.
2022

Topological quantum information theory

Notes.

Coming soon.

Miscellanea

2022

QI, QC, TO, TQFT

etc.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Quantum Computation Theory

The page is for lecture notes on quantum computation theory.

Quantum Computation Theory

2023

Quantum algorithms

Grover search and Simon's algorithm

Quantum phase estimation algorithm

Order-find and Shor's algorithm

Useful information: Page for QIT,

2022

Topological quantum information theory

Notes.

Coming soon.

Miscellanea

2022

QI, QC, TO, TQFT

etc.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Conformal Field Theory

The page is for lecture notes on conformal field theory.

The following are some general references on conformal field theory:

Conformal Field Theory, by Philippe Francesco, Pierre Mathieu, David Senechal.
A Mathematical Introduction to Conformal Field Theory, by M. Schottenloher.
Introduction to Conformal Field Theory-With Applications to String Theory, by Ralph Blumenhagen , Erik Plauschinn.
Conformal Field Theory, by Sergei V. Ketov.
Conformal Invariance and Critical Phenomena, by Malte Henkel.
Applied Conformal Field Theory, by Paul Ginsparg, [arXiv:hep-th/9108028].

There are also some video lectures of CFT avaiable online now:

14/15 PSI - Conformal Field Theory, by Jaume Gomis, Pedro Vieira, Freddy Cachazo.
11/12 PSI - Conformal Field Theory, by Jaume Gomis.
Introduction to conformal field theory, by Tobias Osborne.
Conformal and Supersymmetry, by Christopher Herzog.
Two-dimensional conformal field theory: a primer., by Giuseppe Mussardo.
Laces 2014: Conformal field theories in diverse dimensions., by Luis Fernando Alday.

Conformal field theory

2020

Conformal Field Theory

Pdf version of notes. (incomplete, use at your risk).

Useful information: Page for QIT,

2022

Topological quantum information theory

Notes.

Coming soon.

Miscellanea

2022

QI, QC, TO, TQFT

etc.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Quantum Information Theory

The page is for lecture notes on quantum information theory.

Quantum Information Theory

2020

Basic quantum information theory

Pdf version of notes. (incomplete, use at your risk).

Useful information: Page for QIT,

2022

Topological quantum information theory

Notes.

Coming soon.

Miscellanea

2022

QI, QC, TO, TQFT

etc.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Topological Order

The page is for lecture notes on string theory.

String Theory

2020

Basic string theory

Pdf version of notes. (incomplete, use at your risk).

Homework and solutions: Homework1, Homework2, Homework3, Homework4, Homework5, Homework6, Homework7, Homework8, Homework9, Homework10, Homework11, Homework12, Homework13.

2022

Topological string theory

Notes.

Coming soon.

Miscellanea

2022

QI, QC, TO, TQFT

etc.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Topological Quantum Field Theory

The page is for lecture notes on TQFT.

A page for TQFT.

TQFT

2022
Basic category theory

Basic cateogry theory course: course website. The video (in Chinese) and handwritten lecture notes are available.
- Lec 1: category. [video],[PDF].
  Definition of category; Objects; Morphisms.
- Lec 2: category. [video],[PDF].
  Definition of category; Examples of category.
- Lec 3: category. [video],[PDF].
  Duality principle.
- Lec 4: category. [video],[PDF].
  Definition of functor; example of functors.
- Lec 5: category. [video],[PDF].
  free and forgetful functors; isomorphism and equivalence of categories.
- Lec 5: category. [video],[PDF].
  Free and forgetful functors; isomorphism and equivalence of categories.

Miscellanea

2022

QI, QC, TO, TQFT

etc.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

String Theory

The page is for lecture notes on string theory.

String Theory

2020

Basic string theory

Pdf version of notes. (incomplete, use at your risk).

Homework and solutions: Homework1, Homework2, Homework3, Homework4, Homework5, Homework6, Homework7, Homework8, Homework9, Homework10, Homework11, Homework12, Homework13.

2022

Topological string theory

Notes.

Coming soon.

Miscellanea

2022

QI, QC, TO, TQFT

etc.

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Lecture Notes

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Theoretical Physics

Lecture Notes

A list of lecture notes

Quantum Information theory in a nutshell

Abstract

Basic String Theory

Abstract

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Quantum Information Theory

Some general references

Some useful numerical tools

Quantum Information Theory

Basic quantum information theory

Topological quantum information theory

Miscellanea

QI, QC, TO, TQFT

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Quantum Computation Theory

Quantum Computation Theory

Quantum algorithms

Topological quantum information theory

Miscellanea

QI, QC, TO, TQFT

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Conformal Field Theory

Conformal field theory

Conformal Field Theory

Topological quantum information theory

Miscellanea

QI, QC, TO, TQFT

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Quantum Information Theory

Quantum Information Theory

Basic quantum information theory

Topological quantum information theory

Miscellanea

QI, QC, TO, TQFT

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Topological Order

String Theory

Basic string theory

Topological string theory

Miscellanea

QI, QC, TO, TQFT

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Topological Quantum Field Theory

TQFT

Basic category theory

Miscellanea

QI, QC, TO, TQFT

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

String Theory

String Theory

Basic string theory

Topological string theory

Miscellanea

QI, QC, TO, TQFT

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.