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Woit · 2025-10-20
已登记出处中的最早位置:§39.5 · zh-CN。
来源短摘录与定位
§39.5 · zh-CN · machine_draft · machine-draft-not-reviewed
无限维系统量子化的标准做法是首先进行“正则化(regularization)”,以某种方式修改系统使其仅具有有限维相空间,例如通过引入截断使可能的动量离散且有限。人们通过将态空间和正则对易关系取为海森堡李代数所独有的那些来量子化这一理论,并以某种方式处理相互作用情形(非二次哈密顿量)中的计算困难。
§39.5 · en · machine_draft · machine-draft-not-reviewed
The standard approach to quantization of infinite dimensional systems is to begin with “regularization”, somehow modifying the system to only have a finite dimensional phase space, for instance by introducing cutoffs that make the possible momenta discrete and finite. One quantizes this theory by taking the state space and canonical commutation relations to be the unique ones for the Heisenberg Lie algebra, somehow dealing with the calculational dificulties in the interacting case (non-quadratic Hamiltonian).