87958 - Quantum Field Theory 1

Learning outcomes

At the end of the course the student will have developed an understanding of quantum field theory as the consistent framework unifying quantum mechanics and special relativity. Beginning with the principles of classical field theory, the student will learn how to quantise bosonic and fermionic fields, construct interacting theories such as quantum electrodynamics, study them within perturbation theory, and use Feynman diagrams to compute scattering amplitudes and decay rates.

Course contents

1. Relativity and second quantization: Motivation for quantum fields, Lorentz invariance, natural units, relativistic states, Fock space, creation and annihilation operators.

2. Classical relativistic field theory: Action principle, Euler–Lagrange equations, Hamiltonian formulation, Noether theorem, conserved currents and energy–momentum tensor.

3. The free scalar field: Klein–Gordon equation, canonical quantization, vacuum and multiparticle states, real and complex scalar fields, particles and antiparticles.

4. Cross sections and decay rates: Relativistic normalization, Lorentz-invariant phase space, flux factors, differential and total cross sections, decay widths.

5. The S-matrix and time-ordered products: Interaction picture, Dyson expansion, in and out states, unitarity, Feynman propagator and LSZ reduction.

6. Feynman rules for scalar theories: Wick’s theorem, contractions, connected and disconnected diagrams, momentum-space rules, tree-level scattering and decay processes.

7. Spin-one fields and gauge invariance: Maxwell theory, photon states and polarizations, gauge symmetry, covariant derivatives, gauge fixing, photon propagator and Ward identities.

8. Scalar quantum electrodynamics: Complex scalar fields coupled to electromagnetism, scalar-QED Feynman rules, tree-level amplitudes and gauge invariance.

9. Spinors and the Dirac field: Lorentz representations, Weyl and Dirac spinors, gamma matrices, Dirac equation, helicity and chirality, particles and antiparticles, canonical quantization and spin–statistics.

10. Quantum electrodynamics at tree level: QED Lagrangian, fermionic Feynman rules, spin sums and traces, (e+e- -> mu+mu-), electron–muon scattering, Compton scattering and crossing symmetry, non-relativistic limit.

Readings/Bibliography

Main reference:

1) "Quantum Field Theory and the Standard Model", Matthew D. Schwartz

Additional material:

2) "An Introduction to Quantum Field Theory", M. E. Peskin and D. V. Schroeder

3) "The Quantum Theory of Fields", Volume I, S. Weinberg

4) "Quantum Field Theory" lectures notes by David Tong:

http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

5) "Quantum Field Theory" lecture notes by Timo Weigand:

https://www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf

Teaching methods

Blackboard lectures and exercise sessions.

Assessment methods

Written exam of three hours, with theory/open questions and exercises.

Students with Specific Learning Disabilities (SLD) or temporary/permanent disabilities are advised to contact the corresponding University Office in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/en). The office will be responsible for proposing any necessary accommodations to the students concerned. These accommodations must be submitted to the instructor for approval at least 15 days in advance, and will be evaluated in light of the learning objectives of the course.

Office hours

See the website of Fabio Maltoni