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arXiv · 1101.2653

Geometric extensions of many-particle Hardy inequalities

Douglas Lundholm
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Abstract

Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy inequalities to involve volumes of simplices spanned by a subset of points. Clifford/multilinear algebra is employed to simplify geometric computations. These results and the techniques involved are relevant for classes of exactly solvable quantum systems such as the Calogero-Sutherland models and their higher-dimensional generalizations, as well as for membrane matrix models, and models of more complicated particle interactions of geometric character.

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Douglas Lundholm. 2011-01-13. Geometric extensions of many-particle Hardy inequalities. https://doi.org/10.1088/1751-8113/48/17/175203

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