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Advanced Quantum Field Theory

Code: 44082 ECTS Credits: 6
Degree Type Year Semester
4313861 High Energy Physics, Astrophysics and Cosmology OT 0 2


Joaquim Matias Espona

Use of Languages

Principal working language:
english (eng)


Joaquim Matias Espona
Pere Masjuan Queralt


It is recommended to have followed the course of introduction to Quantum Field Theory of the Master, or at least basic courses on Quantum Field Theory during the undergrate courses.

Objectives and Contextualisation

The main goal of the course is twofold: 1) on one side, to develop a different approach to Quantum Mechanics and Quantum Field Theory based on the Path Integral approach and 2) on the other, to understand and be proficient in the renormalization of a theory. This is a fundamental requisite to arrive to any physical result involving loop diagrams. Besides understanding the concept and renormalization procedure we will focus on its interaction with symmetries and we will conclude by establishing  the renormalization group equations.


  • Formulate and tackle problems, both open and more defined, identifying the most relevant principles and using approaches where necessary to reach a solution, which should be presented with an explanation of the suppositions and approaches.
  • Understand the bases of advanced topics selected at the frontier of high energy physics, astrophysics and cosmology and apply them consistently.

Learning Outcomes

  1. Apply the mechanisms of renormalisation systematically.
  2. Calculate transition widths using lagrangians of effective theories.
  3. Understand the foundations of functional formalism in quantum field theory.


  1. Functional Methods

    1.1 Path Integral in Quantum Mechanics.   

    1.2 Functional Quantization and Path Integral in Quantum Field Theory

    1.3 Symmetries in the functional formalism language

  2. Renormalization Theory

    2.1 Ultraviolet Divergences, conceptual meaning. 

    2.2 Classification of theories according to their renormalization properties

    2.2 Renormallzed perturbation theory

  3. Renormalization and symmetry

    3.1 Spontaneus Symmetry Breaking and linear sigma model: how they should be renormalized.

  4. Aspects of non abelian gauge theories

  5. Renormalization Group Equations


The course will be organized in teaching lectures where the theory of Path Integrals and Renormalization will be developed in full detail.

Students will be encouraged to ask questions during the theory lectures but they also will be asked questions.

Along the lectures a list of problems will be proposed.

It is recommended to follow the course daily including work at home to fully profit and completely understand the concepts discussed.

Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.


Title Hours ECTS Learning Outcomes
Type: Directed      
Theory lectures 45 1.8 1, 2, 3
Type: Autonomous      
Study of theoretical concepts and solution of exercises 82 3.28 1, 2, 3


The evaluation of the course will consist of three blocks:

- A written exam that will count 50% of the note, and with the right to a recovery exam (for 50%).

- Deliveries of problems will be proposed that will count the remaining 40% of the mark.

- Attendance and active participation in class will count 10% of the mark. 

Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Active participation in class 10% 2 0.08 1, 2, 3
Delivery of Solved Problems 40% 15 0.6 1, 2, 3
Final Exam 50% 3 0.12 1, 2, 3
Recovery Exam 50% 3 0.12 1, 2, 3


M. Peskin and D. Schroeder, An introduction to Quantum Field Theory

Lewis H. Ryder, Quantum Field Theory.

Stefan Pokorski, Gauge Field Theories.

C. Itzykson and J. Zuber, Quantum Field Theory

Ta-Pei Cheng and Ling-Fong Li, Gauge theory of elementary particle physics.


No software required.