Elliptic stochastic quantization of Sinh-Gordon QFT

Abstract

The (elliptic) stochastic quantization equation for the (massive) cosh(βϕ)2 model, for the charged parameter in the L 2 regime (i.e. β 2 < 4π), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov space in the continuum to analogous results for Besov spaces on the lattice. As a final result we show as how to use the stochastic quantization equation to verify the Osterwalder-Schrader axioms for the cosh(βϕ)2 quantum field theory, including the exponential decay of correlation functions.

Snowmass White Paper: The Quest to Define QFT

“…More recent reviews include [104][105][106] and a talk [107]. Through a lot of work starting from the late sixties, success has been achieved in rigorously constructing and studying 2d scalar theories with arbitrary polynomial interaction (the so-called P(φ) 2 theories) [88,[108][109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124][125][126][127] (see also book [81], recent papers [128,129], and [130][131][132][133] on other potentials), threedimensional λφ 4 theory [134][135][136][137][138][139][140][141][142] (see also more recent [143][144][145][146][147]), Gross-Neveu theory [148]…”

Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces

“…Non-local type stochastic quantization of the (space cut-off) P (φ) 2 and the Albeverio Høegh-Krohn trigonometric model with d = 2 (for the considerations on this random field, cf., e.g.,[9,13,14,26,[28][29][30][31]36]). 3.…”