用格拉丝曼变量构建费米子神经网络场论，实现超对称量子模型。
Fermions and Supersymmetry in Neural Network Field Theories
- 用格拉丝曼变量扩展中心极限定理，构建费米子神经网络
- 无限宽时实现自由狄拉克旋量，有限宽时出现四费米子相互作用
- 通过超仿射变换引入超对称，适合研究量子场论与超对称模型
我们通过格拉丝曼值神经网络引入费米子神经网络场论。通过将中心极限定理推广至格拉丝曼变量，得到自由理论，在无限宽度下实现自由狄拉克旋量，有限宽度下出现四费米子相互作用。通过破坏费米子与玻色子输出权重的统计独立性，引入约克耦合。通过输入端的超仿射变换，构建一大类相互作用的超对称量子力学与场论模型，实现超空间形式化。
原文摘要 · Abstract (English)
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.
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