
Course unit
QUANTUM FIELD THEORY
SCP7081702, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/02 
Theoretical Physics, Mathematical Models and Methods 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
1 QUANTUM FIELD THEORY 
01/10/2017 
30/11/2018 
MATONE
MARCO
(Presidente)
RIGOLIN
STEFANO
(Membro Effettivo)
GIUSTO
STEFANO
(Supplente)

Prerequisites:

Relativistic quantum mechanics. KleinGordon equation. Dirac equation. Canonical quantization of the scalar and fermionic fields. 
Target skills and knowledge:

The course is focused on the formulation of perturbative quantum field theory. In particular, the expertise and skills to be acquired concerns a good knowledge of the pathintegral formulation of bosonic and fermionic quantum field theories. Part of the course covers the pathintegral formulation of quantum electrodynamics and renormalization theory.
In addition to these skills the student will be able to calculate the contributions up to 2loops in the scalar case (phi^4) and at 1loop in the case of quantum electrodynamics. 
Examination methods:

The examination is oral and concerns the full programm. It starts with the explicit calculation of a Feynman diagram (phi^4 or QED) to be chosen by the student. Then the knowledge and skills of the student will be verified with questions on the various topics of the course. However, the details of the proofs of the theorems introduced in the course are not required. 
Assessment criteria:

The student should demonstrate that she/he acquired a good knowledge of the path integral formulation of quantum field theory. This concerns the general logical structure, the mathematical aspects and the physical motivations. 
Course unit contents:

INTRODUCTION. General aspects of Quantum Field Theories. Perturbative and nonperturbative formulations. Wigner and von Neumann theorems. Spontaneous symmetry breaking. Elitzur theorem. Minkowskian and euclidean formulations.
Overview of the axiomatic formulation: Wightman axioms, Wightman functions, Wightman reconstruction theorem. Schwinger functions and the OsterwalderSchroeder reconstruction theorem.
OPERATOR FORMALISM. Covariance of the Dirac equation. Spin statistics theorem. PCT theorem. The Lehman, Symanzik and Zimmerman theorem.
PATHINTEGRAL IN QUANTUM MECHANICS. Dirac paper at the basis of the Feynman idea. Forced harmonic oscillator. The vacuumvacuum amplitude. Wick rotation. Quadratic lagrangians. BohmAharonov effect.
PATHINTEGRAL FOR SCALAR THEORIES. Functional derivative. General properties of the pathintegral for scalar theories. Convergence methods Feynman propagator. Green functions. Effective action. SchwingerDyson equation. The case of phi^4. Linkedcluster theorem. Euclidean formulation. Computational techniques of functional determinants, the heat equation. Scaling properties of the coupling constant, determinants and anomaly under dilatation. Feynman rules. Computation of some Feynman diagrams for phi^4. Vertex functions and JonaLasinio theorem.
RENORMALIZATION. Ultraviolet and infrared divergences. Dimensional regularization. Superrenormalizable, renormalizable and nonrenormalizable theories. Counterterms. Relation between renormalized and bare vertex functions. Beta function. Landau pole. Ultraviolet and infrared fixed points. Asymptotic freedom and confinement.
FERMIONIC PATHINTEGRAL. Integration over Grassmann numbers. Path integral for the free fermion fields. Feynman rules for spinor fields. Fermion determinants.
QUANTUM ELECTRODYNAMICS (QED): Gauge symmetries. Feynman rules for the gauge fields. Gauge fixing. Evaluation of 1loop Feynman diagrams of QED. Ward identities. Anomalous magnetic moment of the electron.
Renormalization of the QED. 
Planned learning activities and teaching methods:

The teaching method is based on an introductory "abinitio" presentation of the pathintegral formulation of quantum field theory. 
Additional notes about suggested reading:

One aim of the course is to provide a stepbystep derivation of the path integral formulation of quantum field theories. In this respect the course includes several details on some subtle points, including the proof of basic theorems usually not considered in the literature. To this end the references include the lecture notes
https://www2.pd.infn.it/~matone/QFTCourseNotes.pdf
to which the students contributed. Students are encouraged to provide additional contributions. 
Textbooks (and optional supplementary readings) 

Itzykson, Claude; Zuber, JeanBernard, Quantum field theoryClaude Itzykson and JeanBernard Zuber. Mineola: Dover, 2005. Errata corrige available at http://www.lpthe.jussieu.fr/~zuber/ZE_Errata.html

S. Weinberg, The Quantum Theory of Fields. Vol I.. : Cambridge University Press, 2005.

Peskin, Michael E.; Schroeder, Daniel V., An introduction to quantum field theoryMichael E. Peskin, Daniel V. Schroeder. : Westview Press, 1995. Errata corrige available at http://www.slac.stanford.edu/~mpeskin/

Pierre Ramond, Field Theory: A Modern Primer, 2nd Edition. : AddisonWesley, 1989. Errata corrige available at https://www2.pd.infn.it/~matone/

M. Matone & Students, QFT. : , 2018. Notes written by master students, available at https://www2.pd.infn.it/~matone/QFTCourseNotes.pdf

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Working in group
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
 Students are encouraged to write, in depth, the notes of some parts of the course.
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex
Sustainable Development Goals (SDGs)

