Garchinger Maier-Leibnitz-Kolloquium: Geometric Aspects of the Heat-Kernel Formalism

Thursday 20 Nov 2025, 16:15 → 17:15 Europe/Berlin

Lecture Hall, ground floor (west) (LMU building, Am Coulombwall 1, campus Garching)

The heat-kernel formalism is a powerful and versatile tool for analyzing one-loop divergences and asymptotic behaviors of the effective action. After briefly reviewing its standard formulation, we present a more intuitive approach that avoids relying on an ansatz for solving the associated Schrödinger-type equation. Our method leverages Zassenhaus’ formula to treat exponentials of noncommuting operators in a systematic way. Furthermore, we develop a direct configuration-space procedure for extracting ultraviolet divergences, providing an alternative to the conventional momentum-space analysis. Extending the heat-kernel framework, we construct a formulation on a field-space supermanifold that includes both scalar and fermionic coordinates, together with a nonvanishing field-space curvature. As an application, we compute the one-loop effective action for a coupled scalar–fermion system and determine its ultraviolet structure in terms of covariant operators.
The talk is based on the article: V. Gattus and A. Pilaftsis, Supergeometric Quantum Effective Action, Phys. Rev. D 110, 105006 (2024).

Hybrid access via ZOOM:https://lmu-munich.zoom.us/j wd=TWc3V1JkSHpyOTBPQVlMelhuNnZ1dz09
Meeting ID: 984 5733 2925
Passcode: 979953

 

kolloquium-20-11-25.pdf