Topics in high energy and particle theory

Course Description

This is a graduate course (elective) on theoretical aspects of quantum many body system. Quantum field theory is an enormous subject and this course only gets you started. The choice of topics only reflects my personal interest and is biased towards applications in QCD. It aims to develop various analytical and numerical techniques in solving non-perturbative problems in field theory.

Primary topics to be discussed are

(1) Elementary Particle Physics: Fermi’s Golden Rule, Feynman Diagrams, and Scattering Theory

(2) Quantum Field Theory at zero and finite temperature

(3) Symmetries and their spontaneous breaking

(4) Non-perturbative methods in QFT

(5) Quark-hadron phase transition

Some questions of interest

How a potential (to be solved in a Schroedinger Equation) emerges from a QFT? How the LS-coupling term comes about? What are the differences between QFT and a classical field theory? How loop corrections manifest? How equation of motion is realized in QFT? How non-local interactions come in from QFT? How to understand polarizations? How to derive exact relations among Green’s functions based on symmetry constraints?

Marking Scheme

0.6 assignments & projects + 0.4 exam

Aims

By the end of the course, the students will be able to:

  • gain a deeper understanding of many body quantum mechanical systems
  • follow research literatures and reviews

Textbooks

Topics

1st Semester

  • Introduction

    • classification of elementary particles
    • force laws and gauge theory

  • Quantum mechanics I

    • Green’s functions
    • Additions of angular momenta and CG coefficients
    • Solution to the Schroedinger equations: bound and scattering states

  • Particle Physics

    • Fermi’s Golden Rule and Feynman Diagrams
    • Scattering amplitude and optical theorem
    • N-body phase space and Dalitz Decay

  • Quantum field theory

    • Path integral formulation
    • Scalar, Dirac, and gauge fields
    • Symmetries and their fate; Noether’s currents
    • Dynamical mass generation
    • Non-abelian gauge theory

  • Introduction to chiral symmetry

    • chiral rotations
    • PCAC, soft pion theorem, and Gell-Mann Oakes Renner relations
    • effective chiral models

  • Heavy Ion Collisions

    • hadron yields
    • QCD phase diagram

2nd Semester

  • Quantum mechanics II

    • Resonances
    • Dispersion relations
    • Coupled channel models

  • Functional Approach to chiral quark models

    • Introduction to functional approach & Schwinger Dyson Equations
    • Confinement models of QCD

  • Thermal field theory II

    • Classical and quantum cluster / virial expansions
    • Quasi-particles properties and collective effects in medium
    • Mean free time and transport coefficients
    • S-matrix formulation of statistical mechanics

  • Special Topics (depending on time and interest)

    • QCD in Coulomb Gauge
    • Nuclear and Quark matter
    • Effective Model of Gluons
    • Heavy Ion Collisions
    • Constituent quark model
    • Matrix models
    • Potential Models

Preparation and Help

The presentation of physics topics aims to be self-contained, but it is best to come prepared. You should be adept at quantum mechanics. Some knowledge of nuclear and high energy physics would be very helpful but not required. Some familiarity with numerical computation would be a big plus. The most important is the willingness to learn new stuffs. There is a lot to read.

For documentation of codes and works, use of latex and markdown is recommended.

Resources