First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP7081759, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
SC2382, Degree course structure A.Y. 2017/18, A.Y. 2018/19
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ADVANCED QUANTUM FIELD THEORY
Website of the academic structure
Department of reference Department of Physics and Astronomy
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge KURT LECHNER FIS/02

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines FIS/02 Theoretical Physics, Mathematical Models and Methods 6.0

Course unit organization
Period First semester
Year 2nd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 01/10/2018
End of activities 18/01/2019

Examination board
Board From To Members of the board
1 ADVANCED QUANTUM FIELD THEORY 01/10/2018 30/11/2019 LECHNER KURT (Presidente)
MATONE MARCO (Membro Effettivo)

Prerequisites: Students should know the canonical quantization approach of a field theory, in particular of Quantum Electrodynamics, and should be acquainted with the path-integral formalism and the technique of Feynman diagrams.
Target skills and knowledge: The course is aimed to furnish a good knowledge of relativistic quantum field theories, formulated in terms of path-integrals, regarded as theories describing a generic fundamental interaction. Its core are Yang-Mills theories and their perturbative renormalization. Students should learn how to perform explicit quantum computations and to compare the predictions of a theory with observations. On the other hand, they should be able to critically analyze the internal-consistency properties of a theory. Attention will be paid to perturbative and non-perturbative aspects of a quantum field theory.
Examination methods: Solution of a series of proposed problems, followed by an oral examination.
Assessment criteria: Aim of the oral examination is to check the degree of the student's comprehension of the quantum structure of a non-abelian gauge theory, and his ability the expose the arguments with a consequential logic and in a coherent way. The solution of the proposed problems should allow to test the student's ability of facing a problem in an autonomous way, by applying the methods taught during the course, and to check his ability to properly motivate the solutions he proposes.
Course unit contents: 1) INTRODUCTION TO QUANTUM FIELD THEORY. Perturbative and axiomatic aspects.
2) CONSISTENT QUANTUM INTERACTIONS. Coleman-Mandula theorem. Characteristics of interactions versus particle spin. Axion-scalar field duality.
3) CLASSICAL FIELD THEORIES. Action and equations of motion. Universality of couplings. Chiral and Yukawa couplings. Global symmetries and Noether theorem. Theories with local abelian and non-abelian symmetries. Yang-Mills (YM) connection and field strength. Covariant derivative. Conserved currents and covariant currents. Self-interaction of YM fields. Color charge.
4) FUNCTIONAL INTEGRAL METHODS. Brief review of basic concepts. Generating functionals. Analyticity and euclidean space. Background field method. Linear classical symmetries and their quantum implementation. Applications to QED. Determinants of commuting and anticommuting fields. Coleman-Weinberg effective potential and radiative symmetry breaking. Feynman rules for a generic local field theory. Scalar QED.
5) PERTURBATIVE METHOD AND RENORMALIZABILITY. Brief review of dimensional regularization and Feynman-parameters technique. Higher loop corrections. Locality of ultraviolet divergences. Perturbative renormalizability in diverse dimensions.
6) LAMBDA PHI^3 IN D = 6. Explicit one-loop renormalization. Exact one-loop propagator. Counterterms. Beta function and anomalous dimension. Asymptotic freedom and dimensional transmutation. Two-loop renormalization. Nested and overlapping divergences. Cancellation of non-local divergences.
7) QUANTIZATION OF YM THEORIES. Problems related with the quantization of non abelian gauge fields. Faddeev-Popov method and ghost fields. Independence of the gauge fixing. BRST invariance and physical Hilbert space. Slavnov-Taylor identities.
8) PERTURBATIVE ANALYSIS OF YM THEORIES. Feynman rules. Renormalizability. One loop counterterms and their interrelation. The role of ghosts. Beta function and asymptotic freedom. Lambda QCD. Finiteness of N = 4 Super-YM theories.
9) ANOMALIES. Classical and quantum chiral symmetries. Explicit evaluation of the chiral Schwinger action in two dimensions. ABJ anomalies, triangular graphs and extensions to higher dimensions. Anomalous vertex method. Adler-Bardeen theorem. Anomaly cancellation in the Standard Model. Index theorem.
10) INSTANTONS. Semi-classical solutions in field theory. Instantonic configurations. Theta vacua. The U(1) problem. Wilson-loops.
12) AXIOMATIC THEORY. Wightman functions and Schwinger functions. Reconstruction theorem. Triviality of lambda phi^4 theory. Infrared divergences and the problem of charged fields in QED. Goldstone theorem.
Planned learning activities and teaching methods: Mainly frontal lessons. A part of the course is dedicated to the solution of concrete problems, and to the applications of the taught methods in toy models. Special lessons are devoted to illustrate Group Theory at work, applied to the theory of the fundamental interactions.
Additional notes about suggested reading: A series of specific textbooks and references is found on In this page students find also a series of problems proposed for the examination.
Textbooks (and optional supplementary readings)
  • Steven Weinberg, The Quantum Theory of Fields. Cambridge: Cambridge University Press, 2005. Vol. I and II Cerca nel catalogo
  • Claude Itzykson, Jean-Bernard Zuber, Quantum Field Theory. New York: McGraw-Hill Book Co, 1987. Testo avanzato Cerca nel catalogo
  • Mark Srednicki, Quantum Field Theory. Cambridge: Cambridge University Press, 2007. Testo a carattere didattico Cerca nel catalogo
  • Lewis H. Ryder, Quantum Field Theory. Cambridge: Cambridge University Press, 1996. Second edition Cerca nel catalogo
  • John C. Collins, Renormalization. Cambridge: Cambridge University Press, 1984. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Case study
  • Story telling
  • Auto correcting quizzes or tests for periodic feedback or exams
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Latex

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