Higher categorical structures in quantum field theory
Project description
Higher category theory plays an increasingly important role in the mathematical formulation of quantum field theory (QFT). It provides powerful tools to investigate and understand subtle aspects associated with gauge symmetries and thereby opens up new avenues towards designing refined axiomatic frameworks for QFT that are capable to describe quantum gauge theories such as Yang-Mills theory.
This is an interdisciplinary PhD project in the intersection of mathematical physics, algebra and topology. The project could focus either on new developments in higher categorical algebraic QFT or factorization algebras, or on the construction of new examples in these frameworks.
Project published references
M. Benini and A. Schenkel, Operads, homotopy theory and higher categories in algebraic quantum field theory, arXiv:2305.03372 [math-ph].
M. Benini, A. Schenkel and L. Woike, Homotopy theory of algebraic quantum field theories, Lett. Math. Phys. 109, no. 7, 1487 (2019) [arXiv:1805.08795 [math-ph]].
M. Benini, M. Perin and A. Schenkel, Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds, Commun. Math. Phys. 377, no. 2, 971-997 (2019) [arXiv:1903.03396 [math-ph].
M. Benini, G. Musante and A. Schenkel, Green hyperbolic complexes on Lorentzian manifolds, Commun. Math. Phys. 403, no. 2, 699-744 (2023) [arXiv:2207.04069 [math-ph]].
M. Benini, V. Carmona and A. Schenkel, Strictification theorems for the homotopy time-slice axiom, Lett. Math. Phys. 113, no. 1, 20 (2023) [arXiv:2208.04344 [math-ph]].
M. Benini, A. Grant-Stuart and A. Schenkel, Haag-Kastler stacks, arXiv:2404.14510 [math-ph].
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