Exact and Efficient Representation of Totally Anti-Symmetric Functions

Abstract:This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We prove that this ansatz can exactly represent every anti-symmetric and continuous function and the number of basis functions has efficient scaling with respect to dimension (number of particles). The singular locus of the anti-symmetric basis functions is precisely identified.

Classical Analysis and ODEs (math.CA); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)

arXiv:2311.05064 [math.CA]

(or arXiv:2311.05064v3 [math.CA] for this version)

https://doi.org/10.48550/arXiv.2311.05064 Focus to learn more arXiv-issued DOI via DataCite

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