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arXiv · 2606.23650

Position-Space Renormalization and Half-Space Truncations in $\phi^4_4$

Majdouline Borji
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Abstract

In this paper, we study half-space observables in the massive Euclidean $\phi^4_4$ theory. We prove that the renormalized correlators can be multiplied by half-space truncations without requiring any additional renormalization. More precisely, products with smooth approximations of the half-space indicator converge to well-defined distributional limits, uniformly in the ultraviolet cutoff. The proof relies on a position-space renormalization framework for the Wilson--Polchinski flow equation based on a hierarchy of power-counting spaces adapted to the singularity structure of the correlators. This yields uniform power-counting bounds and Besov--H\"older regularity estimates for the renormalized correlators. As a consequence, the correlators converge as the ultraviolet cutoff tends to infinity, and the convergence takes place in explicitly identified Besov spaces.

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Majdouline Borji. 2026-06-22. Position-Space Renormalization and Half-Space Truncations in $\phi^4_4$. https://arxiv.org/abs/2606.23650

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