A Dynamical Yukawa$$_{2}$$ Model

Journal article

We prove local (in space and time) well-posedness for a mildly regularised version of the stochastic quantisation of the Yukawa Euclidean field theory with a self-interacting boson. Our regularised dynamic is still singular but avoids non-local divergences, allowing us to use a version of the Da Prato–Debussche argument (Da Prato and Debussche in Ann Probab 31(4):1900–1916, 2003. https://doi.org/10.1214/aop/1068646370). This model is a test case for a non-commutative probability framework for formulating the kind of singular SPDEs arising in the stochastic quantisation of field theories mixing both bosons and fermions

Authors: Chandra, A; Hairer, M; Peev, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Communications in Mathematical Physics
• Volume: 406
• Issue: 1
• Publication date: 2024-12-09
• DOI: 10.1007/s00220-024-05147-8
• EISSN: 1432-0916
• ISSN: 0010-3616
• Language: English
• Keywords: Mathematics; Noncommutative geometry; Euclidean geometry; Quantum mechanics; Mixing (physics); Statistical physics; Field (mathematics); Geometry; Pure mathematics; Physics; Commutative property; Boson; Yukawa potential; Mathematical physics; Fermion; Euclidean space