
Course unit
ADVANCED QUANTUM FIELD THEORY
SCP7081759, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
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 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Prerequisites:

Students should know the canonical quantization approach of a field theory, in particular of Quantum Electrodynamics, and should be acquainted with the pathintegral 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 pathintegrals, regarded as theories describing a generic fundamental interaction. Its core are YangMills 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 internalconsistency properties of a theory. Attention will be paid to perturbative and nonperturbative 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 nonabelian 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. ColemanMandula theorem. Characteristics of interactions versus particle spin. Axionscalar 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 nonabelian symmetries. YangMills (YM) connection and field strength. Covariant derivative. Conserved currents and covariant currents. Selfinteraction 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. ColemanWeinberg 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 Feynmanparameters technique. Higher loop corrections. Locality of ultraviolet divergences. Perturbative renormalizability in diverse dimensions.
6) LAMBDA PHI^3 IN D = 6. Explicit oneloop renormalization. Exact oneloop propagator. Counterterms. Beta function and anomalous dimension. Asymptotic freedom and dimensional transmutation. Twoloop renormalization. Nested and overlapping divergences. Cancellation of nonlocal divergences.
7) QUANTIZATION OF YM THEORIES. Problems related with the quantization of non abelian gauge fields. FaddeevPopov method and ghost fields. Independence of the gauge fixing. BRST invariance and physical Hilbert space. SlavnovTaylor 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 SuperYM 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. AdlerBardeen theorem. Anomaly cancellation in the Standard Model. Index theorem.
10) INSTANTONS. Semiclassical solutions in field theory. Instantonic configurations. Theta vacua. The U(1) problem. Wilsonloops.
11) DEEP INELASTIC SCATTERING.
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:

During the lectures, detailed references will be given to the topics covered.
Students are encouraged to actively participate in writing course lecture notes. This involvement is very useful for a deeper understanding of the course.
The Quantum Field Theory course notes, available at https://www2.pd.infn.it/~matone/QFTCourseNotes.pdf, include both the required prerequisites and some of the topics covered in this course. 
Textbooks (and optional supplementary readings) 

Steven Weinberg, The Quantum Theory of Fields. Cambridge: Cambridge University Press, 2005. Vol. I and II

Claude Itzykson, JeanBernard Zuber, Quantum Field Theory. New York: McGrawHill Book Co, 1987. Testo avanzato

Mark Srednicki, Quantum Field Theory. Cambridge: Cambridge University Press, 2007. Testo a carattere didattico

Lewis H. Ryder, Quantum Field Theory. Cambridge: Cambridge University Press, 1996. Second edition

John C. Collins, Renormalization. Cambridge: Cambridge University Press, 1984.

Innovative teaching methods: Teaching and learning strategies
 Interactive lecturing
 Working in group
 Questioning
 Problem solving
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex
Sustainable Development Goals (SDGs)

