Bachelor Thesis With Prof. Czakon in 2020
Path integrals, the anharmonic oscillator and Deep Learning
Quantum Field Theory (QFT) in one space-time dimension is simply Quantum Mechanics (QM). It turns out that the basic model of QFT, interacting massive real scalar field theory, becomes the anharmonic oscillator once space dimensions are neglected. The main properties of the QFT system can be studied and undestood on the example of the QM model.
In this thesis, the student will use numerical path integral methods to determine the spectrum of the anharmonic oscillator, determine the presence of Spontaneous Symmetry Breaking, calculate vacuum tunneling amplitudes etc. The novel idea is to use Deep Learning method to optimize the numerical integration.
The student will learn:
- The path integral formulation of Quantum Mechanics
- Numerical simulation methods for path integrals in imaginary time
- Deep learning methods
- Understanding of Quantum Mechanics
- Basic programming ability