C8523 - SYMMETRIES AND PATH INTEGRALS

Learning outcomes

At the end of the course the student will have understood the fundamental role of exact and spontaneously broken symmetries in many areas of physics, including the classification of particles and the description of their interactions. The student will also become familiar with the path integral formulation of quantum mechanics and quantum field theory, which is the framework for setting up the perturbative analysis of interacting quantum field theories.

Course contents

Part I (Cicoli)

• Symmetries to classify particles: Lie groups and Lie algebras; generators and representations; SU(N), Lorentz, and Poincarè groups; fields with different spin and multiplets as representations in one-particle Hilbert space. 

• Symmetries to constrain dynamics: Noether's theorem in field theory and examples.

• Symmetries to describe interactions: interacting Abelian and non-Abelian gauge theories at tree level.

• Spontaneous breaking of symmetries to introduce mass scales and relation to new physics: Goldstone's theorem; Abelian and non-Abelian Higgs mechanism.

Part II (Bastianelli)

• Action principle for particles

• Path integrals in quantum mechanics

• Correlation functions and generating functionals

• Interacting theories and perturbative expansion

• Functional integrals for fermionic systems

• Functional integrals for gauge theories
  

Readings/Bibliography

Lecture notes, available on Virtuale.

Suggested books for further study:
J. Zinn-Justin, "Path Integrals in Quantum Mechanics", (Oxford Graduate Texts, 2010)

Teaching methods

Lectures delivered at the blackboard

Assessment methods

Oral Examination – Approximate duration: 30 minutes.

The oral examination normally consists of two general questions on the topics covered during the course (one question for each module). Students are expected to provide a thorough and critical discussion of the subject matter. The final grade will be based on the accuracy and clarity of the presentation, the ability to develop well-reasoned arguments and analyses, and the capacity to identify and explain the most conceptually significant aspects of the topics discussed.

Assessment Criteria

18–23/30: elementary knowledge of the course topics.
24–26/30: adequate knowledge of the course topics.
27–30/30: good knowledge and solid command of the course topics.
30/30 cum laude: excellent knowledge of the course topics, outstanding critical and analytical skills, full command of the disciplinary terminology, and a remarkable degree of independent thinking and elaboration.

 

Students with Specific Learning Disabilities (SLD) or temporary/permanent disabilities are advised to contact the University Office responsible in a timely manner (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will be responsible for proposing any necessary accommodations to the students concerned. These accommodations must be submitted to the instructor for approval at least 15 days in advance, and will be evaluated in light of the learning objectives of the course.

 

 

 

 

Office hours

See the website of Fiorenzo Bastianelli

See the website of Michele Cicoli