Infopaket

Anomalies in Gauge Theories

ОК 13

Обов’язкова дисципліна для ОП

Second

2023/2024

3 Semester

6

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.

Full-time form

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.

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.

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.

Lectures, workshops, independent work.

Tests, thematic control of independent work, examination work.

Ukrainian