Papers

We develop a rigorous framework for the description of general local composite observables in Euclidean quantum field theories. The approach is nonperturbative and combines renormalisation group ideas with techniques of stochastic analysis. Via renormalisation dictated by sufficiently precise approximate solution theory of corresponding flow equations, we construct various local observables of the sine–Gordon model on the full space up to \(\beta^2 < 6 \pi\), including highly singular ones such as vertex fields \(\exp (i \alpha \phi (y))\) in the optimal Wick regime \(| \Re e (\alpha) | < 4 \pi / \beta\) and derivatives of arbitrarily high order, i.e. \(\partial^{\mu} \phi (y)\) for any multiindex \(\mu \in \mathbb{N}^2_0\). Applications of the approach include a direct proof of smoothness of observable-inserted correlation functions, and verification that the constructed objects satisfy a version of the prefactorization algebra axioms adapted to our setting.

We present a new, simple and self-contained technique for proving a mass gap for Euclidean quantum field theories in the high-temperature regime using the stochastic quantisation approach. As an application, we establish exponential decay of spatial correlations for the fractional \(\Phi^4\) model on the plane in the Wick-ordering regime. The key idea is to analyse the propagation of perturbations using the linearised stochastic quantisation equation. Spatial propagation is controlled by an auxiliary random walk, while the potentially destabilising effect of the renormalised nonlinearity is controlled by combining dissipative energy estimates for the nonlinear dynamic with the Boué–Dupuis variational formula.