This work provides the fundamental theoretical framework for molecular cavity quantum electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonians under the electronic state truncation. We conjecture that such ambiguity arises because not all operators are consistently constrained in the same truncated electronic subspace for both gauges. We resolve this ambiguity by constructing a unitary transformation operator that properly constrains all light-matter interaction terms in the same subspace. We further derive an equivalent and yet convenient expression for the Coulomb gauge Hamiltonian under the truncated subspace. We finally provide the analytical and numerical results of a model molecular system coupled to the cavity to demonstrate the validity of our theory.

中文翻译：

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分子腔量子电动力学中规矩歧义的解决

这项工作通过解决电子态截断下的库仑规和偶极规哈密顿量之间的规范模糊性，为分子腔量子电动力学提供了基本的理论框架。我们猜想会出现这种歧义，因为并非所有操作员都在两个仪表的同一截短电子子空间中始终受到约束。我们通过构造一个统一变换运算符来解决这种歧义，该运算符可以适当地约束同一子空间中的所有光-质相互作用项。我们进一步为截断子空间下的库仑量规哈密顿量导出了一个等效且方便的表达式。最后，我们提供了与腔耦合的模型分子系统的分析和数值结果，以证明我们的理论的有效性。