# Archive

This is a repo for dumping notes & homework, released under CC-BY-NC-SA 4.0. 

PDF is usually compiled using `xelatex` & `biber`. However, if there are Feynman diagrams created with `tikz-feynman`, then it should be compiled with `lualatex`. The LaTeX engine to use is specified with a _magic comment_, e.g.
```latex
% !TeX TS-program = lualatex
```

For PDFs, please go to [Releases](https://github.com/bryango/Archive/releases/latest); they are also hosted on:
- https://bryango.github.io/resources/archive/, a simple tree view built with pages;
- https://cdn.jsdelivr.net/gh/bryango/resources@gh-pages/archive/, auto-generated by jsDelivr.

PDFs are generated by Github actions & workflows; for implementations, see `.github/`. 

## Strings2020 `strings`

String Theory, Spring 2020, by Prof. Chi-Ming Chang @ Tsinghua. 

**Contents**:
1. Classical spinning string, conformal transformations, bc CFT & Noether's theorem, SO(n) free fermion CFT and current algebra;
2. BRST current of bosonic string, detailed calculations of OPE, normal ordering ambiguity, linear dilaton CFT, bosonic strings on S^3 & Dirac's quantization, and anomalous current from curvature;
3. Perturbative calculation of beta functions, classical 11D gravity & Freund–Robin compactification, SUSY counting with Killing spinors, superspace formalism, and mixed diffeo-axial anomaly in standard model;
4. Vertex operators, contraction of exponentials, symmetry of 3-point functions, D0-string scattering calculated with CKV & image charge, and gluon-tachyon scattering;
5. Compact scalar with winding, zero point fixing, partition function and modular invariance, orbifold & twisted sectors, torus bc path integral, and torus propagator as a trace;
6. Type 0 superstring from consistency conditions, GSO projections & partition functions, KK mechanism & 5D theory, fiberwise T-duality from path integral, dilaton shift, cylinder diagram factorization & only one coupling in string theory;
7. T-duality of heterotic strings, Wilson line background & symmetry breaking, string junctions & SUSY counting, 2-pt / 3-pt functions in AdS/CFT from boundary-to-bulk propagators and conformal symmetry. 

## AdvancedQFT2020 `advqft`

Advanced Quantum Field Theory, Spring 2020, by Prof. Wenbin Yan & Prof. Dan Xie @ Tsinghua. 

**Contents**:
1. Noether's theorem & Poincare algebra;
2. Finite gauge transformation & Chern-Simons form, Faddeev-Popov quantization for particles & strings;
3. BRST transformation in Yang-Mills theory, and BRST quantization of point particle.

### `gauge`

A non-technical note on the geometry of gauge theory, including bundles and connection, with discussions about tetrad formalism and spin connection in gravity. 

## ThermalFieldTheory2020 `thermal`

Finite Temperature Field Theory, Spring 2020, by Prof. Lian-Yi He @ Tsinghua

**Contents**:
1. Thermal propagator of free theory, from path integral;
2. Pure QED partition function in covariant gauge, with Faddeev-Popov quantization & mode expansions;
3. QCD partition function from Feynman diagrams, with tricks to compute Matsubara sums;
4. Ward identity with hard thermal loop (HTL), decomposition of transverse self-energy using projections, and HTL in QCD;
5. Correlations of Pauli spinors, using effective formalism & perturbative expansions, with full calculations of Matsubara sums & frequency integral; results expressed in spectral functions.

## SpinorGR `spinor`

An intuitive introduction of spin structure & spinor in general relativity (GR), with discussions of physical motivations, and a sketch of Witten's proof of the positive energy theorem. Written as the final paper for Differential Geometry, a course in Fall 2019 given by Prof. Hui Ma @ Tsinghua.

## AlgebraicTopology2020 `algtop`

Algebraic Topology, Spring 2020, by Prof. Si Li @ Tsinghua

Incomplete due to early withdrawn, but contains some nice commutative diagrams.