Fermions and Supersymmetry in Neural Network Field Theories

TL;DR

This paper introduces a novel framework for neural network field theories incorporating fermions and supersymmetry using Grassmann-valued neural networks, enabling new models of quantum fields with supersymmetric properties.

Contribution

It develops Grassmann-valued neural networks for fermionic fields and constructs supersymmetric models through super-affine transformations, extending neural network field theory capabilities.

Findings

Realization of free Dirac spinor at infinite width

Implementation of four fermion interactions at finite width

Introduction of supersymmetric quantum models via super-affine transformations

Abstract

We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac spinor at infinite width and a four fermion interaction at finite width. Yukawa couplings are introduced by breaking the statistical independence of the output weights for the fermionic and bosonic fields. A large class of interacting supersymmetric quantum mechanics and field theory models are introduced by super-affine transformations on the input that realize a superspace formalism.