# Questions tagged [commutator]

A mathematical construct quantifying the difference in effect of applying two operators in two alternate successions. It is the defining product of a Lie algebra, the efficient underlying description of Lie groups, of use in several areas of physics, most notably quantum field theory.

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### Obscure Calculations in Foldy-Wouthuysen Transformation (electron in EM field)

I'm studying the Foldy-Wouthuysen Transformation on Bjorken-Drell's book and I got stuck strying to replicate some calculations. First of all, introducing the transformation $\psi'=e^{iS}\psi$ we get ...
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### What does "not applying the CCR" mean exactly?

I've seen mentioned in a number of posts that some relations do or do not apply depending on whether one is "applying the CCR". For example, In Relationship between normal-ordered vacuum ...
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### Common eigenstate of incompatible observables

In many resources I have seen that incompatible observables cannot have a common eigenbasis set, but may share one or few eigen states. I followed the thread Can incompatible observables share an ...
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### An interpretation for Propagator $D(x-y)$

When I learn QFT I always see that when we consider the causality problem in QFT, at first we may try to compute the propagator $D(x-y)$ for spacelike distance $(x-y)^2<0$, which is nonzero. An ...
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### Normalization of one particle state wave function in fock space - commutator

In deriving the 1/$\sqrt{N!}$ normalization factor the first step is looking at the one particle state (see image below). I am confused about how we got from the first line to the second? Maybe I am ...
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### How does Sakurai reduce a product to a commutator?

The following section is from Modern Quantum Mechanics by Sakurai; can any one help me finding out how this is done? In contrast, if we follow approach 2, we obtain \begin{align} \vert\alpha\...
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### Why does $e^{-H}\partial_j e^{H} = \partial_j + \partial_jH$?

I apologize if this is a dumb question but I have really thought about this a while and I can’t understand it. I have tried to prove this using the power series of the exponential function but I did ...
how did they reach the conclusion that quantization of the Poisson brackets $(A,B)$ was equal to the commutator $\frac{1}{i\hbar}[A,B]$ in quantum mechanics? so the quantum equations of motion ...