Teaching plan for the course unit



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General information


Course unit name: Quantum Field Theory

Course unit code: 568427

Academic year: 2019-2020

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


Face-to-face and/or online activities



-  Lecture





(Approximate distribution.)


-  Lecture with practical component





(Approximate distribution.)

Supervised project


Independent learning




Competences to be gained during study


— Capacity to effectively identify, formulate and solve problems, and to critically interpret and assess the results obtained.

— Knowledge forming the basis of original thinking in the development or application of ideas, typically in a research context.

— Capacity to apply the acquired knowledge to problem-solving in new or relatively unknown environments within broader (or multidisciplinary) contexts related to the field of study.

— Capacity to integrate knowledge and tackle the complexity of formulating judgments based on incomplete or limited information, taking due consideration of the social and ethical responsibilities involved in applying knowledge and making judgments.

— Capacity to communicate conclusions, judgments and the grounds on which they have been reached to specialist and non-specialist audiences in a clear and unambiguous manner.

— Skills to enable lifelong self-directed and independent learning.

— Capacity to communicate, give presentations and write scientific articles in English on fields related to the topics covered in the master’s degree.

— Capacity to critically analyze rigour in theory developments.

— Capacity to acquire the necessary methodological techniques to develop research tasks in the field of study.

— Capacity to analyze and interpret a physical system in terms of the relevant scales of energy.

— Capacity to identify relevant observable magnitudes in a specific physical system.

— Capacity to understand and apply general gravitation theories and theories on the standard model of particle physics, and to learn their main experimental principles (specialization in Particle Physics and Gravitation).

— Capacity to critically analyze the results of calculations, experiments or observations, and to calculate possible errors.





Learning objectives


Referring to knowledge

— Learn to renormalise loops, scalar theories and QED.

— Understand the consequences of exact and approximate symmetries.



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 Klein-Gordon 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; Källén-Lehmann spectral representation; Collisions and S-matrix; LSZ reduction formula; Feynman diagrams, and KL and KLS formulas; 1PI diagrams and self-energy

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; Schwinger-Dyson equations; Conservation laws: Ward-Takahashi identity

5. Renormalisation

*  Ultraviolet divergences and renormalised theories; Renormalised perturbation theory; Dimensional regularisation; Feynman parameters; One-loop renormalisation of Ø^4 theory; One-loop renormalisation of QED; Counterterms; Two-loop renormalisation of Ø^4 theory; Callan-Symanzik equation; Evolution of coupling constants



Teaching methods and general organization


Lectures. Expository classes. Problem-solving sessions.



Official assessment of learning outcomes


Assessment is based on problem-solving activities carried out throughout the course.
Repeat assessment consists of an examination in June.