Introduction to Quantum Field Theory II

Course objectives

GENERAL OBJECTIVES: Aim of the course is advancing with the study of the fundamental aspects of Quantum Field Theory, starting from the topics covered in the course “Introduction to Quantum Field Theory 1”. In particular, the course will i) give a thorough and systematic discussion of relativistic scattering theory; ii) illustrate the application of perturbation theory beyond tree level; iii) discuss the procedure of renormalization of a field theory. The know-how acquired by attending this course is key for a complete and deep understanding of more advanced courses in Quantum Field Theory, and especially for students enrolled in the “Particle and Astroparticle Physics” curriculum. SPECIFIC OBJECTIVES: A - Knowledge and understanding OF 1) Knowing the procedure of renormalization of a QFT and its specific application to QED. OF 2) Understanding perturbation theory beyond tree level. OF 3) Knowing relativistic scattering theory and understanding its more formal aspects. B – Application skills OF 4) Knowing Feynman rules for the computation of decay rates and cross sections at 1-loop in perturbation theory. C - Autonomy of judgment OF 5) Being able to apply the know-how acquired during this course to the formulation of the Standard Model of fundamental interactions, and to the study of the Renormalization Group and of Effective Field Theories. D – Communication skills OF 6) Being able to discuss topics in QFT with the required mathematical rigor while keeping the various approximations done under control. E - Ability to learn OF 7) Being able to read and make use of textbooks and scientific articles with the purpose of further investigating the topics covered in this course.

Channel 1
ROBERTO CONTINO Lecturers' profile

Program - Frequency - Exams

Course program
[1] Scattering Theory - Adiabatic approximation - Partial wave decomposition - Non-relativistic limit and effective potential - Optical Theorem - LSZ reduction formulas - Computation of physical processes at tree level [2] Spinors and Symmetries - Clifford Algebra and spinorial representations of the Lorentz group - Dirac, Weyl and Majorana spinors - Discrete Symmetries: Parity, Charge conjugation, Time-reversal [3] Rinormalization: the example of QED - Anomalous magnetic moment of the electron - Ward identities - Beta-function and running coupling - Computation of physical processes at 1 loop level [4] Short introduction to Effective Field Theory - Fermi theory of beta decay - Euler-Heisenberg effective Lagrangian
Prerequisites
Students should have a fundamental knowledge of math and physics courses taught in the Bachelor Degree (Laurea Triennale), in particular they should be familiar with: basic aspects of analytical mechanics (Lagrangians, Hamiltonians, actions, equations of motion and their invariance, conserved quantities), classical electrodynamics, Maxwell equations, special relativity. They should also have basics knowledge of quantum field theory (canonical quantization, quantum electrodynamics, Feynman rules).
Books
M. Peskin, D. Schroeder, An Introduction to Quantum Field Theory, Perseus Books S. Weinberg, The Quantum Theory of Fields, vol.1, Cambridge Univ. Press
Teaching mode
Lectures and training sessions in classroom.
Frequency
Lectures and training sessions in the classroom.
Exam mode
The exam consists of a written and an oral session. During the written session, students will be asked to perform the calculation of a cross section or a decay width. The oral session covers the whole programme of the course and is done at the blackboard. In particular, students should be able to give a logical derivation of the results. The evaluation criteria include: - the correctness of the arguments reported in the written and oral sessions - the ability in solving the written session - the clarity and the mathematical rigour in the oral session The final score is the result of a global assessment of the written and oral sessions.
Bibliography
M. Peskin, D. Schroeder, An Introduction to Quantum Field Theory, Perseus Books S. Weinberg, The Quantum Theory of Fields, vol.1, Cambridge Univ. Press
Lesson mode
Lectures and training sessions in the classroom.
  • Lesson code10620705
  • Academic year2025/2026
  • Coursecorso|33602
  • CurriculumFundamental Interactions: Theory and Experiment
  • Year1st year
  • Semester2nd semester
  • SSDFIS/02
  • CFU6
  • Subject areaTeorico e dei fondamenti della fisica