Subject: QUANTUM FIELD THEORY (A.A. 2020/2021)
Unit Quantum Field Theory
Theory and Foundations of Physics (lesson)
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.
Knowledge and Understanding.
At the end of the course the student will own the basic elements and tools of quantum field theory.
Applying Knowledge and Understanding.
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.
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.
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
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
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. NOTE: The lectures and exercise sessions will happen either in presence or via remote learning depending on the evolution of the COVID-19 emergency.
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. NOTE: The exams will happen either in presence or via web-conference depending on the evolution of the COVID-19 emergency.
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.
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.