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arXiv · 1411.3670

Extension of distributions, scalings and renormalization of QFT on Riemannian manifolds

Nguyen Viet Dang
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Abstract

Let $M$ be a smooth manifold and $X\subset M$ a closed subset of $M$. In this paper, we introduce a natural condition of \emph{moderate growth} along $X$ for a distribution $t$ in $\mathcal{D}^\prime(M\setminus X)$ and prove that this condition is equivalent to the existence of an extension of $t$ in $\mathcal{D}^\prime(M)$ generalizing some previous results of Meyer and Brunetti--Fredenhagen. When $X$ is a closed submanifold of $M$, we show that the concept of distributions with moderate growth coincides with weakly homogeneous distributions of Meyer. Then we renormalize products of distributions with functions tempered along $X$ and finally, using the whole analytical machinery developed, we give an existence proof of perturbative quantum field theories on Riemannian manifolds.

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Nguyen Viet Dang. 2014-11-13. Extension of distributions, scalings and renormalization of QFT on Riemannian manifolds. https://arxiv.org/abs/1411.3670

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