Tobias Osborne: QFT 2016
Rigorous path integral approach to quantum field theory from Leibniz Universität Hannover
About This Course
Tobias Osborne's QFT course provides a comprehensive, mathematically rigorous treatment of quantum field theory with particular emphasis on the path integral formulation and gauge theories. These 18 lectures cover classical field theory through gauge fixing and Faddeev-Popov quantization.
📐 Mathematical Rigor
Detailed derivations with careful mathematical treatment
🔁 Path Integrals
Strong focus on functional integral methods
🔄 Gauge Fields
Extensive treatment of gauge theories and fermions
Course Structure
Part I: Foundations (Lectures 1-7)
- • Classical field theory and Lagrangian formalism
- • Symmetries and Noether's theorem
- • Canonical quantization of scalar fields
- • Causality and microcausality
- • Symmetry representations in QFT
Part II: Interactions (Lectures 8-13)
- • Interacting field theory
- • Feynman diagrams and rules
- • Vacuum bubbles and connected diagrams
- • S-matrix and scattering theory
- • Comprehensive overview and synthesis
Part III: Fermions (Lectures 14-18)
- • The Dirac field and Dirac equation
- • Solutions to the Dirac equation
- • Quantizing the Dirac field (canonical anticommutation relations)
- • Fermionic Fock space and creation/annihilation operators
- • Interacting fermions and bosons (QED, Yukawa theory)
Lectures 1-7: Classical & Quantum Foundations
Introduction
Course overview, historical context, why QFT, basic setup and goals
Video Lecture
Quantum field theory, Lecture 1: Introduction
Course introduction and motivation for QFT
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Classical Field Theory
Lagrangian formalism, Euler-Lagrange equations, Hamilton's principle for fields
Video Lecture
Quantum field theory, Lecture 2: Classical Field Theory
Foundation of classical field theory and action principles
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Symmetries
Continuous symmetries, Noether's theorem, conserved currents and charges
Video Lecture
Quantum field theory, Lecture 3: Symmetries
Symmetries in field theory and Noether's theorem
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Field Quantization
Canonical quantization, equal-time commutation relations, Hamiltonian formalism
Video Lecture
Quantum field theory, Lecture 4: Field Quantization
From classical to quantum fields via canonical quantization
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Building and Solving the Quantum Scalar Field
Fock space construction, creation/annihilation operators, mode expansion
Video Lecture
Quantum field theory, Lecture 5: Building and solving the quantum scalar field
Complete solution of the free scalar field
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Causality
Microcausality, commutators at spacelike separation, locality in QFT
Video Lecture
Quantum field theory, Lecture 6: Causality
Causal structure of quantum field theory
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Representing Symmetries in QFT
Unitary representations, Wigner's theorem, Poincaré group in QFT
Video Lecture
Quantum field theory, Lecture 7: Representing symmetries in QFT
Symmetry representations and Poincaré invariance
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lectures 8-13: Interactions & Feynman Diagrams
Interactions
Interaction picture, time evolution, Dyson series, perturbation theory setup
Video Lecture
Quantum field theory, Lecture 8: Interactions
Introduction to interacting field theories
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Interactions and Feynman Diagrams
Wick's theorem, contractions, graphical representation of perturbation terms
Video Lecture
Quantum field theory, Lecture 9: Interactions and Feynman diagrams
From Wick's theorem to Feynman diagrams
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Feynman Diagrams
Momentum space diagrams, propagators, vertices, combinatorial factors
Video Lecture
Quantum field theory, Lecture 10: Feynman diagrams
Detailed construction of Feynman diagrams
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Feynman Rules and Vacuum Bubbles
Complete Feynman rules, vacuum diagrams, connected vs disconnected
Video Lecture
Quantum field theory, Lecture 11: Feynman rules and vacuum bubbles
Systematic derivation of Feynman rules
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
The S Matrix
Scattering matrix, LSZ reduction formula, asymptotic states, in/out states
Video Lecture
Quantum field theory, Lecture 12: The S matrix
S-matrix theory and scattering amplitudes
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Overview So Far
Comprehensive review of lectures 1-12, synthesis of key concepts, preparation for fermions
Video Lecture
Quantum field theory, Lecture 13: Overview so far
Mid-course review and synthesis
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lectures 14-18: The Dirac Field & Fermions
The Dirac Field
Dirac equation, spinor structure, gamma matrices, Lorentz covariance
Video Lecture
Quantum field theory, Lecture 14: The Dirac Field
Introduction to the Dirac field and spinors
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
The Dirac Field and Its Solution
Solving the Dirac equation, plane wave solutions, spinor normalization
Video Lecture
Quantum field theory, Lecture 15: The Dirac Field and its solution
Solutions to the Dirac equation
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
The Quantum Dirac Field (1/2)
Canonical anticommutation relations, fermionic Fock space, spin-statistics
Video Lecture
Quantum field theory, Lecture 16: The quantum Dirac Field (1/2)
Quantization of the Dirac field - Part 1
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
The Quantum Dirac Field (2/2)
Fermionic propagators, Wick's theorem for fermions, charge conjugation
Video Lecture
Quantum field theory, Lecture 17: The quantum Dirac Field (2/2)
Quantization of the Dirac field - Part 2
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
QFT for Interacting Fermions and Bosons
QED, Yukawa theory, fermion-boson interactions, Feynman rules for fermions
Video Lecture
Quantum field theory, Lecture 18: QFT for interacting fermions and bosons
Interactions between fermions and bosons
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
How to Use This Course
🎯 For Rigorous Study
Use Tobias Osborne alongside MIT 8.323 for a comprehensive, mathematically rigorous treatment.
- • Lectures 1-7 complement MIT Part I
- • Lectures 4-7 pair with MIT Part II
- • Lectures 8-13 align with MIT Part III
- • Lectures 14-18 correspond to Dirac Field
🔄 Alternative Perspective
When MIT lectures are unclear, watch the corresponding Osborne lecture for a different approach.
- • Different notation and conventions
- • More detailed derivations in some areas
- • Strong path integral emphasis
- • European physics tradition vs MIT style
Recommended Study Paths
Path 1: Conceptual → Rigorous
DrPhysicsA for visual intuition
Susskind for physical understanding
Tobias Osborne for mathematical rigor
MIT Parts I-V for comprehensive coverage
Path 2: Dual Rigorous Approach
Watch Tobias Osborne lecture on a topic
Read corresponding MIT text material
Work through problem sets from both sources
Review with DrPhysicsA for visual consolidation
Osborne vs MIT vs Susskind
| Aspect | Tobias Osborne | MIT 8.323 | Susskind |
|---|---|---|---|
| Mathematical Level | Very rigorous | Very rigorous | Moderate, intuitive |
| Primary Approach | Path integrals + canonical | Canonical + path integrals | Physical principles |
| Pace | Moderate, thorough | Fast, compressed | Slow, conceptual |
| Best For | Second perspective, path integrals | Primary text, problem sets | First introduction, intuition |
| Gauge Theory Coverage | Extensive (18 lectures basis) | Comprehensive (Part V) | Conceptual overview |
Additional Resources
- • Full YouTube Playlist:QFT 2016 by Tobias Osborne
- • Lecturer:Prof. Tobias Osborne, Leibniz Universität Hannover
- • Course Website:Institute for Theoretical Physics, Hannover
- • Related Topics:Quantum Information, Many-Body Physics, Advanced QFT