Geometric extensions of many-particle Hardy inequalities

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.

Revised version. 28 pages

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Cited by in corpus (9)

• Optimal Hardy Weight for Second-Order Elliptic Operator: An Answer to a Problem of Agmon
• Some contributions to many-body quantum mathematics
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• Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics
• Schrödinger operators with negative potentials and Lane-Emden densities
• Hardy and Rellich inequalities for anisotropic p-sub-Laplacians
• Drift-diffusion equations on domains in ${\mathbb{R}}^d$: essential self-adjointness and stochastic completeness
• Optimal Hardy inequalities associated with multipolar Schrödinger operators