Exact and Efficient Representation of Totally Anti-Symmetric Functions
Classical Analysis and ODEs
2025-01-10 v2 Computational Physics
Quantum Physics
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.
Keywords
Cite
@article{arxiv.2311.05064,
title = {Exact and Efficient Representation of Totally Anti-Symmetric Functions},
author = {Ziang Chen and Jianfeng Lu},
journal= {arXiv preprint arXiv:2311.05064},
year = {2025}
}