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arXiv · 2204.04326

Perturbative renormalization of $ϕ_4^4$ theory on the half space $\mathbb{R}^+ \times\mathbb{R}^3$ with flow equations

Majdouline Borji·Christoph Kopper
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Abstract

In this paper, we give a rigorous proof of the renormalizability of the massive $ϕ_4^4$ theory on a half-space, using the renormalization group flow equations. We find that five counter-terms are needed to make the theory finite, namely $ϕ^2$, $ϕ\partial_zϕ$, $ϕ\partial_z^2ϕ$, $ϕΔ_xϕ$ and $ϕ^4$ for $(z,x)\in\mathbb{R}^+\times\mathbb{R}^3$. The amputated correlation functions are distributions in position space. We consider a suitable class of test functions and prove inductive bounds for the correlation functions folded with these test functions. The bounds are uniform in the cutoff and thus directly lead to renormalizability.

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Majdouline Borji, Christoph Kopper. 2022-04-08. Perturbative renormalization of $ϕ_4^4$ theory on the half space $\mathbb{R}^+ \times\mathbb{R}^3$ with flow equations. https://doi.org/10.1063/5.0097164

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