Nielsen, Matilde (2026) An Investigation of an Alternative Perturbed Gaussian Integration with application to 0D QFT. Bachelor's Thesis, Physics.
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Abstract
The path integral reduces to an ordinary perturbed Gaussian integral in 0-dimensional quantum field theory (QFT). However, even for simple physical systems this integration is not easy to perform. In a hand-out Dror Bar-Natan and Roland van der Veen propose an alternative way of evaluating this integral, which could possibly facilitate solving certain perturbed Gaussian integrals. In this thesis we will investigate this alternative method of integration. We start off by presenting all the details behind the derivation of the method, and realizing for what cases this new integration should agree with the ordinary one. It is then superficially explored which integration properties one should expect to hold for this new integration. Afterwards, some 0-dimensional QFT examples are tested out, for which good agreement with the expected results is concluded. Furthermore, we generalize this integration to Grassmann variables in order to possibly apply the method to the path integrals of “fermionic fields”. Finally, we show how certain Feynman diagrams, the vacuum graphs, come to light when considering this alternative approach to the perturbed Gaussian integral. In short, this exploration of the alternative integration seems to suggest that this new operation agrees well with anticipated results, and could possibly provide a novel mathematical interpretation of the path integral.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Pallante, E. and Veen, R.I. van der |
| Degree programme: | Physics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 29 Jul 2026 13:52 |
| Last Modified: | 29 Jul 2026 13:52 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37476 |
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