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A variational approach for the 2D Abelian Yang-Mills-Higgs measure
Nikolay Barashkov, Ajay Chandra, Ilya Chevyrev +2
We use the Boué-Dupuis variational method to construct the Abelian Yang-Mills-Higgs measure on the two-dimensional torus with polynomial Higgs potentials, giving, to our knowledge,…
A PDE approach to the 2D Yang-Mills measure
Ilya Chevyrev, Tom Klose, Abdulwahab Mohamed
We introduce the concept of rough additive functions, which extends rough paths theory to line integrals of distributional 1-forms. In the context of gauge theory, we use this noti…
Locality of rough path lifts
Ilya Chevyrev, Emilio Ferrucci
Every Hölder continuous path admits a geometric rough path lift by the Lyons--Victoir extension theorem. A natural question that emerges when lifting more than…
From path integral quantization to stochastic quantization: a pedestrian's journey
Dario Benedetti, Ilya Chevyrev, Razvan Gurau
We give two novel proofs that the path integral and stochastic quantizations of generic scalar Euclidean quantum field theories are equivalent. Our proofs rely on Taylor interpolat…