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arXiv · 1707.02939

Wick Ordering and Kinetic Energy Renormalization for Lévy White Noise Fields

Rodrigo Vargas Le-Bert
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Abstract

Let $S=\mathbb{T}^d$ be a torus and $μ$ the probability distribution of a Lévy white noise field $x:S\rightarrow\mathbb{R}$. Using projective limit measures we address the problem of making sense of $\mathrm{e}^{-T(x)}$, where $T(x) = \int_S \lvert\nabla x(s)\rvert^2 \mathrm{d}s$ is the kinetic energy, as a function in $L^1(μ)$. We start by making sense of $T(x)$ itself as a sort of distribution, which is achieved by a generalization of Wick ordering. Then we specify to the case of a $Γ$ field, finding that Wick ordering does not eliminate all divergences. Higher order renormalization would be required, but the model seems to be non-renormalizable.

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Rodrigo Vargas Le-Bert. 2017-07-10. Wick Ordering and Kinetic Energy Renormalization for Lévy White Noise Fields. https://arxiv.org/abs/1707.02939

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