
Course unit
QUANTUM FIELD THEORY
SCP7081702, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
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 
Prerequisites:

Relativistic quantum mechanics. Classical filed equations and canonical quantization of the scalar and fermionic fields. Basic QED. 
Target skills and knowledge:

The path integral formulation of quantum mechanics and of relativistic field theories and its applications to the perturbative solution of scalar field theories and quantum electrodynamics. Basic conceptual and technical notions of renormalization and the renormalization group. 
Examination methods:

The examination is oral and it will consist of the discussion of one of the problems assigned during the course and of some general questions on the topics of the course, including the derivation of the main results. 
Assessment criteria:

Knowledge and understanding of the path integral formulation of quantum field theories in the perturbative approximation, and the ability to apply the general concepts to compute simple physical quantities in scalar field theory and quantum electrodynamics. 
Course unit contents:

Path integrals in quantum mechanics and its generalization to relativistic quantum field theories. Correlation functions and their euclidean continuation. Relation between correlation functions and the Smatrix: the LehmannSymanzikZimmermann reduction formula. Equivalence of the pathintegral and operator formalism.
Selfinteracting scalar field theory: the perturbative expansion, functional derivation of the Feynman rules, generating functions and effective action. The fermionic pathintegral. The definition of the pathintegral for gauge theories: QED.
Divergences in quantum field theories. Dimensional regularization. Counterterms and renormalization. Oneloop renormalization for the scalar field theory with quartic coupling and for QED. An introduction to renormalization at higher loops. The Renormalization Group: computation of the betafunction and of the anomalous dimension in scalar field theory and QED. The role of symmetries: Ward identities, gauge symmetries, the WardTakahashi identity in QED. Renormalization and the floating cutoff: an introduction to the WilsonPolchinski equation. 
Planned learning activities and teaching methods:

Lectures and weekly assignments. 
Textbooks (and optional supplementary readings) 

Srednicki, Mark A., Quantum field theoryMark Srednicki. Cambridge: Cambridge university press, 2007.

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.


