Teaching plan for the course unit



Close imatge de maquetació




General information


Course unit name: Quantum Field Theory

Course unit code: 574642

Academic year: 2021-2022

Coordinator: Bruno Julia Diaz

Department: Department of Quantum Physics and Astrophysics

Credits: 3

Single program: S



Estimated learning time

Total number of hours 75


Face-to-face and/or online activities



-  Lecture

Face-to-face and online




-  Lecture with practical component

Face-to-face and online



Independent learning






Students are advised to have completed or be enrolled in the subject Advanced Quantum Mechanics. 



Learning objectives


Referring to knowledge

  1. To develop a broad and unified perspective based on symmetries on fundamental and emergent field theories. 

  2. To become familiar with the basic tools of formalism, like construction of Lorentz invariant representations and Lagrangians and identification of invariants and conserved charges. 

  3. To understand the fundamentals of gauge symmetries. 



Teaching blocks


1. Symmetries in mechanics


  1. Definition of invariance

  2. Physical consequences of invariance 

  3. Invariance in classical mechanics 

  4. Invariance in quantum mechanics (Wigner theorem) 

  5. Galilean relativity and Galileo group 

  6. Einstein relativity and Poincare group 

  7. Internal symmetries

  8. Local symmetries

2. Relativistic wave equations


  1. Representations of the Poincare group 

  2. Wave equation for spin 0 (Klein-Gordon equation)

  3. Wave equation for spin ½ (Dirac equation) and its properties

  4. Wave equation for spin 1: the photon

3. Second Quantization


  1. Fock space

  2. Field operators and their transformation properties

  3. Locality and discrete symmetries 

  4. CPT theorem

  5. Lagrangian formalism and Noether theorem

  6. Canonical quantization

4. Gauge Theories


  1. Quantization of the electromagnetic field

  2. Minimal coupling and examples

  3. Perturbation theory

  4. Ward identities

  5. Topological invariants



Teaching methods and general organization


  1. Lectures where theoretical contents of the subject are presented. 

  2. Practical exercise classes in which students may participate. 

  3. Activities related to the subject suggested by the teaching staff. 



Official assessment of learning outcomes



Examination-based assessment

A final written exam covering the contents of the course.



Reading and study resources

Consulteu la disponibilitat a CERCABIB


Landau, L. and Lifschitz, E. Course of Theoretical Physics: Vol. I, III, and IV. Addison-Wesley (English ed.)

 Weinberg, S. (1995). The quantum theory of fields (Vol. 1). Cambridge university press.  EnllaƧ