Anomalies in Gauge Theories

Course: Quantum field theory

Structural unit: Faculty of Physics

Title
Anomalies in Gauge Theories
Code
ОК 13
Module type
Обов’язкова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2021/2022
Semester/trimester when the component is delivered
3 Semester
Number of ECTS credits allocated
6
Learning outcomes
Know the basic concepts of quantum anomaly theory such as chiral and large-scale anomalies. Know the basic methods of calculating quantum anomalies. Know the basic infrared properties of quantum anomalies. Know the basic spectral properties of the Dirac operator. Be able to calculate triangular diagrams that describe a chiral anomaly. Be able to solve equations of chiral kinetic theory that describe anomalous charge transport. Be able to calculate the values ​​of quantities and charges that reduce the calibration anomalies in the Standard Model. Be able to analyze the infrared properties of the Dirac operator in external calibration fields.
Form of study
Full-time form
Prerequisites and co-requisites
1. Know the basic principles of high energy physics, quantum field theory, calibration theories, statistical physics, know the basics of the Standard Model. 2. Be able to use quantum field charting techniques and calculate functions Green. 3. Have the skills to search for and study specialized literature, solutions algebraic and differential equations, work with interactive and multimedia means, interaction with colleagues during training.
Course content
Topic 1. Chiral anomaly in (1 + 1) -dimensional theory. Topic 2. Decomposition of a neutral peony into two photons. Topic 3. Chiral anomaly in quantum chromodynamics. Topic 4. Infrared properties of anomalies. Topic 5. Dirac operator theorem and chiral anomaly. Topic 6. Effective action of Weiss-Zumino interaction Nambugoldstone bosons. Topic 7. Instantons, anomalies and θ-vacuum. Topic 8. Anomalous violation of large-scale invariance.
Recommended or required reading and other learning resources/tools
1. Peskin M.E., Schroeder D.V. Inroduction to quantum field theory. Reading: PERSEUS BOOKS PUBLISHING, 1995. 2. Weinberg S., The quantum field theory, V. 2. Cambridge: CAMBRIDGE UNIVERSITY PRESS, 1996. 4. Treiman S.B., Jackiw R., Zumino B., Witten E. Current algebra and anomalies. Princeton: PRINCETON UNIVERSITY PRESS, 1985. 5. Bertlmann R.A. Anomalies in quantum field theory. Oxford: CLARENDON PRESS, 1996.
Planned learning activities and teaching methods
Lectures, workshops, independent work.
Assessment methods and criteria
Tests, thematic control of independent work, examination work.
Language of instruction
Ukrainian

Lecturers

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Departments

The following departments are involved in teaching the above discipline