Mathematical introduction to quantum field theory 1100-4`MIQFT

Plan of the course

1. Geometry of Minkowski spaces and curved spacetimes.
2. Algebraic formulation of quantum mechanics
3. Haag-Kastler and Wightman axioms
4. Second quantization formalism
5. Elements of classical field theory
6. Canonical commutation relations
7. Klein-Gordon equation, also on curved spacetimes
8. Quantization of scalar field on stationary spacetimes
9 Path integrals
10 Renormalization in the presence of external fields

Student's work load:

Lectures: 30 h -- 2ECTS

Exercise classes 30 h -- 2ECTS

Preparation for lectures: 30 h -- 1 ECTS

Preparation for the exam: 30 h -- 1 ECTS

Main fields of studies for MISMaP

mathematics
physics

Type of course

elective monographs

Mode

Blended learning

Prerequisites (description)

The course is addressed primarily to students of Theoretical Physics, but it will be accessible to students of other specializations, and also to Mathematics studdents. It will not require advanced background in Mathematics. Its prerequisites are Quantum Mechanics I and Classical Mechanics, as well as elementary background on Hilbert spaces, distributions and differential geometry.

Course coordinators

Jan Dereziński

Learning outcomes

Knowledge: Understanding of foundations of quantum field theory.

Skills: Solving simple problems about quantum field theory.

Attitude: Precision of thinking and striving towards deeper understanding of theoretical formalism used in physics

Assessment criteria

Homework problems and oral exam

Practical placement

does not apply

Bibliography

S. Weinberg: Theory of Quantum Fields

C. Itzyckson, G. Zuber: Quantum field theory

Jan Dereziński,
https://www.fuw.edu.pl/~derezins/qft-lectures.pdf

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1100-4`MIQFT in USOSweb