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Instructors: Univ.-Prof. Dr. Martin Reuter
Event type:
Lecture
Displayed in timetable as:
Hours per week:
4
Credits:
6,0
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Contents:
Content:
In many areas of modern research, ranging from condensed matter theory to high energy physics and quantum gravity, quantization by functional integrals has superseded the traditional approach of canonical quantization, i.e., the one that is adopted by almost all introductory texts and lectures on quantum mechanics and Quantum Field Theory.
The lecture in WiSe 2023/24 provides an elementary introduction to the concept of functional integrals, with applications to nonrelativistic quantum mechanics.
The lecture series is continued in SoSe 2024 with a detailed exposition of functional integrals in Quantum Field Theory, along with an introduction to a number of related modern developments, the Functional Renormalization Group in particular.
Both parts of this lecture series are fully self-contained.
Topics (WS 2023/24):
- From canonical to functional integral quantization
- General properties of functional integrals
- Application to elementary systems (free particle, harmonic oscillator, general quadratic system,...)
- Spectra and wave functions
- Oscillator with time dependent frequency
- Topologically nontrivial configuration spaces
- Semiclassical methods
- Euclidean functional integrals
- Instantons
- Tunneling processes
Recommended reading list:
- L. S. Schulman, Techniques and Applications of Path Integration, J. Wiley
- A. Das, Field Theory: A Path Integral Approach, World Scientific
- C. Grosche, F. Steiner, Handbook of Feynman Path Integrals, Springer
- G. Roepstorff, Path Integral Approach to Quantum Physics, Springer
- B. Felsager, Geometry, Particles and Fields, Springer
- H. Kleinert, Path Integrals, World Scientific
- E. Gozzi, E. Cattaruzza, C. Pagani, Path Integrals for Pedestrians, World Scientific
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