Project III 2025-26

Relativistic Quantum Mechanics

Arthur Lipstein

Description

Quantum mechanics and special relativity are two pillars of modern physics. In this project, students will learn about various challenges that arise when combining relativity and quantum mechanics and how they are resolved by quantum field theory. For a concise overview, see chapter 1 of Srednicki's book. In more detail, students will learn about

  • the Klein-Gordon equation (section 8.1 of "Modern Quantum Mechanics" by Sakurai)
  • the Dirac equation (section 8.2 of Sakurai)
  • Identical particles and second quantisation (Chapter IX of "Quantum Mechanics" by Landau and Lifshitz)
  • basic quantum field theory (section 8.1.5 of Sakurai, chapter 39 of Srednicki)

    • Students will have the opportunity to explore other related directions if time permits. For example, they can derive corrections to the energy levels of hydrogen from the Dirac equation (section 8.4 of Sakurai), learn about the spin-statistics theorem (chapter 5 of Tong's lecture notes on QFT), or the CPT theorem (chapter 40 of Srednicki).

    Suggested Pre-requisites

    Mathematical Physics II

    Special Relativity & Electromagnetism II

    Suggested Co-requisites

    Quantum Mechanics III