In order to find quantum corrections to the de Sitter entropy, a new approach to higher loop Feynman integral computations on the sphere is presented. Arbitrary scalar Feynman integrals on a spherical background are brought into the generalized Euler integral (A-hypergeometric series/GKZ systems) form by expressing the massive scalar propagator as a bivariate radial Mellin transform of the massless scalar propagator in one higher dimensional Euclidean flat space.
This formulation is expanded to include massive and massless vector fields by construction of similar embedding space propagators. Vector Feynman integrals are shown to be sums over generalized Euler integral formed of underlying scalar Feynman integrals. Granting existence of general spin embedding space propagators, general spin Feynman integrals are shown, by the construction of a "master" integral, to also be sums over generalized Euler integral representations of scalar Feynman integrals. Finding exact embedding space propagator expressions for fields of integer spin ≥ 2 and half integer spin is left to future work.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/sjnw-dw40 |
| Date | January 2024 |
| Creators | Bandaru, Bhavya |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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