The wavefront set and its applications in quantum field theory (2024)
This work explores the relevance of the wavefront set in Quantum Field Theory (QFT) with a focus on addressing the problem of divergences. It begins with an introduction to QFT, detailing the interaction picture, Dyson series, and Wick’s theorems, which are fundamental tools for understanding particle interactions and the emergence of divergences. The work transitions into an examination of distribution theory, providing the necessary mathematical framework to handle the infinities associated with these divergences. The wavefront set is defined and examined through the lens of Hörmander's condition, with detailed analyses of wavefront sets for common distributions. The wavefront sets of both the Wightman and the Feynman propagator are also explored, demonstrating the relevance of these mathematical tools in the field. The final section discusses the integration of the wavefront set into a more modern version of the Epstein-Glaser renormalization method, emphasizing the practical benefits and challenges of using the wavefront set in this context. The study concludes with reflections on the potential of this approach to offer deeper insights and more robust solutions to the persistent issues of renormalization in QFT.