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DIEGO TRANCANELLI
Professore Associato
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Fisica
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Insegnamento: Quantum Field Theory
Physics - Fisica (Offerta formativa 2022)
Obiettivi formativi
Why QFT?
Quantum field theory (QFT), a pillar of modern physics, plays a central role in our understanding of Nature. First of all, it provides the best description we have of the fundamental interactions, such as the electro-weak and strong forces that form the Standard Model of particle physics. In particular, quantum electrodynamics, the QFT of electromagnetism, not only represents the theoretical foundation of all atomic physics and chemistry, but is also responsible for astoundingly precise theoretical predictions of physical observables, as never before seen in the history of science. At the same time, QFT represents one of the most powerful tools to approach complex systems and more recent applications of QFT can also be found in cosmology and in the study of dark matter and dark energy. Finally, it is impossible to underestimate the importance of QFT in mathematics and mathematical physics, in particular in relation to geometry and topology.
At the end of the course the student will own the basic elements and tools of quantum field theory. The gained knowledge shall allow the reading of advanced textbooks and research papers and will leave the student well-equipped for more advanced courses like Advanced QFT.
This is a fundamental course for all students interested in a theoretical curriculum.
Prerequisiti
Requirements: The mathematical knowledge of the three-year curriculum in physics (calculus and mathematical methods of physics). Quantum mechanics, elements of special relativity and classical field theory.
An effort will be made to review all necessary requirements when needed.
Programma del corso
The course consists of 24 2-hour lessons, including the discussion and correction of exercises.
Topics to be covered include:
1) Introduction and motivation for QFT
2) Review of classical field theory
3) Scalar fields, canonical quantization
4) The vacuum in QFT
5) Causality and propagators
6) Spinors (Dirac, Weyl and Majorana), canonical quantization
7) Path integrals in quantum mechanics and QFT
8) Interactions
9) LSZ formula
10) Cross sections and decay rates
11) Yukawa theory
12) Gauge fields, canonical and path integral quantization
13) QED processes
14) Radiative corrections and divergences
15) Renormalization, counterterms, regularization schemes
16) Renormalization of QED
17) Multiloop diagrams
18) Optical theorem and unstable particles
Metodi didattici
The course is made of 48 hours of lectures and some sessions of proposed exercises. Some of them are homework and some will be solved in class.
Testi di riferimento
The literature on QFT textbooks is huge, but I will mostly use (in no particular order):
1) The Quantum Theory of Fields, by S. Weinberg
2) Quantum Field Theory, by C. Itzykson and J. Zuber
3) An Introduction to Quantum Field Theory, by M. Peskin and D. Schroeder
4) Modern Quantum Field Theory, A Concise Introduction, by T. Banks
5) Quantum Field Theory , by M. Srednicki
6) Quantum Field Theory in a Nutshell, by A. Zee
7) https://www.damtp.cam.ac.uk/user/tong/qft.html, by D. Tong
I am not going to follow a specific textbook for the whole duration of the course. Instead, at the beginning of each lecture I am going to tell you the relevant chapters of the books I have used for that particular topic.
Verifica dell'apprendimento
The grade will be based on an oral exam over all the program covered in the course and on the correction of a homework set distributed during the semester and due one week before the chosen date for the oral exam.
Risultati attesi
This course is designed for the first-year students of the Master Course in physics. The aim is to offer the basic concepts and tools of quantum field theory, also in view of possible further studies.
Knowledge and understanding:
At the end of this course, it is expected that the students dominate the basic notions of Quantum Field Theory, such as the notion of field (with spin 0, 1/2 and 1) and its quantization, the interaction among fields, their scattering processes and their renormalization.
Ability to apply knowledge and understanding:
The students will be able to understand research papers on the topic of the course, at least in their basic aspects (introductory sections).
Autonomy of judgement:
The students will be able to choose the best methods and approaches for the description and treatment of a given physical system.
Communication skills:
The students will learn the the typical language of Quantum Field Theory, and to communicate effectively the concepts in this realm.
Learning skills:
The students will acquire learning strategies to break a typical problem in Quantum Field Theory down to its basic components and to assimilate complex topics.