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• W2895032979 abstract "We present a new construction of the Euclidean $Phi^4$ quantum field theory on $mathbb{R}^3$ based on PDE arguments. More precisely, we consider an approximation of the stochastic quantization equation on $mathbb{R}^3$ defined on a periodic lattice of mesh size $varepsilon$ and side length $M$. We introduce a new renormalized energy method in weighted spaces and prove tightness of the corresponding Gibbs measures as $varepsilon rightarrow 0$, $M rightarrow infty$. Every limit point is non-Gaussian and satisfies reflection positivity, translation invariance and stretched exponential integrability. These properties allow to verify the Osterwalder--Schrader axioms for a Euclidean QFT apart from rotation invariance and clustering. Our argument applies to arbitrary positive coupling constant, to multicomponent models with $O(N)$ symmetry and to some long-range variants. Moreover, we establish an integration by parts formula leading to the hierarchy of Dyson--Schwinger equations for the Euclidean correlation functions. To this end, we identify the renormalized cubic term as a emph{distribution} on the space of Euclidean fields." @default.
• W2895032979 created "2018-10-12" @default.
• W2895032979 creator A5002317619 @default.
• W2895032979 creator A5007048442 @default.
• W2895032979 date "2018-10-03" @default.
• W2895032979 modified "2023-10-11" @default.
• W2895032979 title "A PDE construction of the Euclidean $Phi^4_3$ quantum field theory" @default.
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