Quantum field theory 1

A.Y. 2020/2021
Overall hours
Learning objectives
The course provides an introduction to relativistic quantum
field theory, its theoretical foundations, and its application to the
perturbative computation of scattering processes.
Expected learning outcomes
The course provides an introduction to relativistic quantum
field theory, its theoretical foundations, and its application to the
perturbative computation of scattering processes.

Risultati di apprendimento attesi (inglese )
At the end of this course the student will know how to

Decouple the dynamics of coupled finite-and infinite-dimensional
system in terms of normal coordinates

Obtain a classical field as the continuum limit of a system of coupled
harmonic oscillators

Construct a relativistic classical field theory for scalar, vector and
spin 1/2 fields

Determine the conserved currents in the presence of both internal and
space-time symmetry, specifically the enrrgy-momentum tensor

Quantize a free scalar field and construct its Fock space

Quantize a Fermi field

Obtain the time evolution of a quantum field theory from its path

Compute the path integral and propagator for a free field theory of
Bosons or Fermions

Write down the path integral for an interacting field theory and use
it to calculate Green functions

Relkate aplitudes to Green functions through the reduction formula

Determine the Feynman rules for a given theory from the path integral

Compute amplitudes and cross-sections for simple processes

Understand the origin of divergences in perturbative computations, and
how to tame them through regularization and renormalization

Determine the Feynman rules for a renormalized field theory

Determinare le regole di Feynman per una teoria rinormalizzata

Understand under which conditions a theory is renormalizable or not,
and what it means
Course syllabus and organization

Single session

Lesson period
Second semester
Course syllabus
--Classical field theory
+ normal coordinates
+ the continuum limit and classical fields
+ equations of motion
+ Noether's theorem
--Field quantization: free fields
+quantisation of the scalar field and Fock space
+several degrees of freedom: the charged field and the spin-one field
+fermionic fields: the Dirac field
--Interacting fields
+interactions and time evolution
+the path integral
+the propagator
+the path integral for fermions
+the interaction vertex
+the reduction formula
+Feynman rules
--Leading order computation of physical processes:
+computation of the amplitude
+kinematics and reference frames
+the cross-section
+divergences and their meaning
+renormalised perturbation theory
Prerequisites for admission
Nonrelativistic quantum mechanics. Special relativity. The Lagrangian formulation of classical mechanics.
Teaching methods
The course consists of 42 hours of blackboard lectures, during which the basic theory and techniques of quantum field theory are presented, and some applications are worked out. A teaching assistant is available for helping the students with questions and for discussing problems.
Teaching Resources
Reference textbook

M. Maggiore: A Modern Introduction to Quantum Field Theory; Oxford
University Press, 2005

Further reading

M.E. Peskin, D.V. Schroeder: An Introduction to Quantum Field Theory; Addison-Wesley, 1995
S. Weinberg: The Quantum Theory of Fields: Vol. I (foundations); Cambridge University Press, 1995
A. Zee, Quantum Field Theory in a Nutshell; Princeton University Press, 2010
V. Radovanovic: Problem Book in Quantum Field Theory; Springer, 2007
Assessment methods and Criteria
The final exam consists of a written two-hour-long test and a half-hour oral exam. In the written test the student is asked to work out standard applications, such as deriving the Feynman rules for a given theory and use them to calculate amplitudes. In the oral exam, the student is asked to discuss one of the topics from the course syllabus, chosen on the spot. All previous written exams are available (with solutions) from the instructor's website.
Lessons: 42 hours
Professor: Forte Stefano
every day after 12.30
Physics department, room DC/I/6