General information 
Course unit name: Quantum Field Theory
Course unit code: 568427
Academic year: 20192020
Coordinator: Bartolome Santiago Fiol Nunez
Department: Department of Quantum Physics and Astrophysics
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface and/or online activities 
51 
 Lecture 
Facetoface 
42 

(Approximate distribution.) 

 Lecture with practical component 
Facetoface 
9 

(Approximate distribution.) 
Supervised project 
40 
Independent learning 
59 
Competences to be gained during study 
— Capacity to effectively identify, formulate and solve problems, and to critically interpret and assess the results obtained.

Learning objectives 
Referring to knowledge — Learn to renormalise loops, scalar theories and QED.

Teaching blocks 
1. Classical field theory
* Motivations: from the quantum theory of relativistic particles to the quantum theory of fields; Classical field theory; Functional derivative; Lagrangian and Hamiltonian formulations; Noether’s theorem and conservation laws; Poincaré group generators
2. Quantisation of free field theory
* Harmonic oscillator and real scalar field; Canonical quantisation of real scalar fields; Klein Gordon equation; Microcausality; Propagators for the KleinGordon equation: retarded propagator and Feynman propagator; Particle creation by a classical source; Complex scalar field; Quantisation of the Dirac field; Quantisation of the electromagnetic field
3. Interactive field theory
* The Ø^4 interaction; Interaction picture; Time evolution operator; Correlation function; Wick’s theorem; Feynman diagrams; Feynman rules; Feynman rules for QED; Disconnected diagrams; KällénLehmann spectral representation; Collisions and Smatrix; LSZ reduction formula; Feynman diagrams, and KL and KLS formulas; 1PI diagrams and selfenergy
4. Path integral quantisation
* Path integrals and quantum mechanics; Functional quantisation of the scalar field; Correlation function; Feynman rules for Ø^4 theory; Function generator; Interactions; Functional quantisation of spinor fields; SchwingerDyson equations; Conservation laws: WardTakahashi identity
5. Renormalisation
* Ultraviolet divergences and renormalised theories; Renormalised perturbation theory; Dimensional regularisation; Feynman parameters; Oneloop renormalisation of Ø^4 theory; Oneloop renormalisation of QED; Counterterms; Twoloop renormalisation of Ø^4 theory; CallanSymanzik equation; Evolution of coupling constants
Teaching methods and general organization 
Lectures. Expository classes. Problemsolving sessions. 
Official assessment of learning outcomes 
Assessment is based on problemsolving activities carried out throughout the course. 
Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
https://cercabib.ub.edu/iii/encore/record/C__Rb1330066?lang=cat
Ramond, Pierre. Field theory : a modern primer. 2a ed. Reading : AddisonWesley, cop. 1989.
Srednicki, Mark. Quantum field theory, Cambridge : Cambridge University Press, 2007