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产生及湮没算符.
物理学中,湮没算符(Creation and annihilation operators)是将处于特定状态中的多个粒子,其粒子数下降1的算符;产生算符则是将处于特定状态中的多个粒子,其粒子数增加1的算符,产生算符也是湮没算符的伴算符(adjoint)。按照不同的课题,问题中的粒子类型也各有不同。举例来说,在量子化学与多体理论中,产生与湮没算符的作用对象常为电子。
湮没与产生算符在量子谐振子的场合中,特别指的是阶梯算符。在这样的场合,升算符诠释为产生算符,将一能量量子加到振子系统,对于降算符也是相同的类比。它们可以用来代表声子。在物理学与化学的分支学科里,使用这些算符而不是波函数的方法称之为二次量子化。
产生与湮没算符背后的数学与出现在量子谐振子中的阶梯算符的式子相同。举例来说,湮没与产生算符对于同一状态的交换子等于一;其他的交换子皆为零。
产生与湮没算符的概念对于自由场论来说是有良好定义的,然而在相互作用量子场论(interacting QFTs)中,它们只能在相互作用绘景(interaction picture)中有所定义;而根据哈格定理(Haag's theorem),相互作用绘景是不存在的。
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