Teaching plan for the course unit



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General information


Course unit name: Gauge Theory: the Standard Model

Course unit code: 568436

Academic year: 2019-2020

Coordinator: Domenec Espriu Climent

Department: Department of Quantum Physics and Astrophysics

Credits: 6

Single program: S

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Estimated learning time

Total number of hours 150


Face-to-face and/or online activities



-  Lecture





-  Lecture with practical component




Supervised project


Independent learning




Competences to be gained during study


Acquire a capacity for analysis, comprehension and abstract thought.

Acquire problem-solving skills.

Capacity to work in teams.

Critical reasoning.

Logical mathematical and formal reasoning.

Capacity for independent learning.





Learning objectives


Referring to knowledge

Begin to develop an understanding of the technicalities and common characteristics of gauge theories, such as quantum electrodynamics (QED), quantum chromodynamics (QCD) and electroweak theory.

Understand and be able to easily use the characteristic techniques of field theories with gauge symmetry: Feynman diagram, dimensional regularisation, renormalisation groups.
Learn the fundamental principles of the standard model in elemental interactions: structure, symmetries, radiative corrections and renosmalisation.
Learn other key aspects of field theories in fundamental interactions.



Teaching blocks



*  Euclidean and Minkowski conventions 

Summary of path integral methods
Effective action and functional methods
The phenomenon of spontaneous symmetry breaking
Classical abelian and non-abelian invariance

Classical solutions in gauge theories

*  The 2d O(3) sigma model

The ’t Hooft-Polyakov monopole
Instantons in QCD
Zero modes and chiral symmetry breaking

Introduction to QCD

*  Why QCD

Classical QCD lagrangian
Global symmetries in QCD and their realisation
The U(1)_A anomaly
The theta vacuum
Anomaly cancellation

Quantisation of gauge theories

*  Covariant quantisation: Faddeev-Popov formalism in QED and QCD

Ghosts in Yang-Mills and their interpretation
Feynman rules
BRST symmetry
Ward and Slavnov-Taylor identities
Spontaneous symmetry breaking and renormalisability
R_\xi gauges and modified Slavnov-Taylor identities

Radiative corrections in gauge theories

*  Divergent structure of gauge theories

Renormalisation and counter-terms in QCD
The meaning of the renormalisation procedure
Calculation of the beta function in QCD
The renormalisation group and fixed points
The R parameter and renormalisation ambiguities
Decoupling of heavy quarks

The limits of perturbation theory

*  Confinement

Infrared divergences: inclusive and exclusive processes
The operator product expansion
Power corrections to R

Gauge structure of the electroweak theory

*  Summary of known results

Gauges and gauge fixing; Physical states
Mass generation and spontaneous symmetry breaking
Fermion masses
The CKM matrix
Semileptonic decays

The electroweak theory beyond tree level

*  FCNC and the GIM mechanism

CP symmetry and CP violation in kaons and other neutral systems
The Gilman-Wise effective lagrangian

Radiative corrections in electroweak theory

*  Effective couplings

The on-shell scheme
Precision observables



Teaching methods and general organization


Lecturers explain the different teaching blocks during face-to-face sessions.

Students solve weekly set exercises.



Official assessment of learning outcomes


Independent study: questions, activities, attitude in class, formality and quality of submitted exercises: 10%

Set exercises: 50%

Final examination: 40%

Repeat assessment criteria: repeat assessment follows the same criteria as regular assessment and consists of a final exam.


Examination-based assessment

Written final exam: 100%

Repeat assessment criteria: repeat assessment follows the same criteria as regular assessment and consists of a final exam.