A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one)

• URL: http://arxiv.org/abs/2510.11431v1
• Date: Mon, 13 Oct 2025 14:03:47 GMT
• Title: A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one)
• Authors: Liang Fu,
• Abstract summary: Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science.<n>We introduce a universal and exact representation of continuous antisymmetric functions by lifting them to continuous symmetric functions defined on an enlarged space.<n>Our results provide a rigorous mathematical foundation for efficient representations of fermionic wavefunctions and enable scalable and systematically improvable neural network solvers for many-electron systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them to continuous symmetric functions defined on an enlarged space. Building on this lifting, we obtain a \emph{parity-graded representation} of fermionic wavefunctions, expressed in terms of symmetric feature variables that encode particle configuration and antisymmetric feature variables that encode exchange statistics. This representation is both exact and minimal: the number of required features scales as $D\sim N^d$ ($d$ is spatial dimension) or $D\sim N$ depending on the symmetric feature maps employed. Our results provide a rigorous mathematical foundation for efficient representations of fermionic wavefunctions and enable scalable and systematically improvable neural network solvers for many-electron systems.

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