The Gross-Neveu model is a quantum field theory model of Dirac fermions in two
dimensions with a quartic interaction term. Like Yang-Mills theory in four dimensions, the …

We prove local (in space and time) well-posedness for a mildly regularised version of the
stochastic quantisation of the\(\hbox {Yukawa} _ {{2}}\) Euclidean field theory with a self …

On ad-dimensional Riemannian, spin manifold (M, g) we consider non-linear, stochastic
partial differential equations for spinor fields, driven by a Dirac operator and coupled to an …

We present two approaches to establish the exponential decay of correlation functions of
Euclidean quantum field theories (EQFTs) via stochastic quantization (SQ). In particular we …

We introduce a theory of non-commutative $ L^{p} $ spaces suitable for non-commutative
probability in a non-tracial setting and use it to develop stochastic analysis of Grassmann …

We present a new approach to noncommutative stochastic calculus that is, like the classical
theory, based primarily on the martingale property. Using this approach, we introduce a …

The subject of the thesis is the study of singular stochastic partial differential equations
(SPDEs), in connection with questions of mathematical physics and constructive field theory …

We present a construction of the Gibbs measure of the fractional Φ4 model of Euclidean
quantum field theory in three-dimensions. The measure is obtained as a perturbation of the …

We introduce Wilson Itô diffusions: a class of random fields on Rd that change continuously
along a scale parameter via a Markovian dynamics with local coefficients. Described via …