canonical momentum equation transformation

正则动量、哈密顿正则方程

canonical (adj.)

early 15c., "according to ecclesiastical law," from Medieval Latin canonicalis, from Late Latin canonicus "according to rule," in Church Latin, "pertaining to the canon" (see canon (n.1)). Earlier was canonial (early 13c.). General sense of "conformed or conforming to rule" is from 1560s. Meaning "of or belonging to the canon of Scripture" is from 1560s; hence "of admitted excellence" (1550s).

正则是什么概念?

“具有某种良好性质的”。

正则系综是稳定的,正则矩阵是可逆的,正则变换是保持正则形式不变的,正则性是用来表达光滑程度的,正则图是完全的,正则文法是DFA可识别的,正则项是可以防止过拟合的…

If something has canonical status, it is accepted as having all the qualities that a thing of its kind should have.

—— 《柯林斯英汉双解大词典》

也就是说,正则的意思其实就是形容这玩意儿具有各种人们期许的良好性质而已。具体指什么要根据具体的情景。

导出页面自 Analytical mechanics by Louis N. Hand, Janet D. Finch (z-lib.org).pdf

正则方程良好性质