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4 questions
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Regarding physical phenomena related to operators of the form $\exp(x\partial_x)$ [duplicate]
I am studying exponential operators, for example, of the form $\exp(x \partial_x)$. Do these operators appear or model any physical phenomena? or are they just abstract entities?
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Scaling dimension and inversions
Defining an inversion transformation in coordinates as
$$
x^\mu\rightarrow \mathcal{I}x^\mu = \frac{x^\mu}{x^2}, \tag1
$$
if we want to study these transformations on tensor operators $\mathcal{O}$ we ...
- 1,607
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What does the exponentiated generator of scale transformation do when it acts on a function? [duplicate]
We know that $d/dx$ is the generator of translation in the sense that $$e^{ad/dx}f(x)=f(x+a)\tag{1}$$ which can be easily be proved from the Taylor series of $f(x+a)$.
Studying the very basics of ...
- 12.3k
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Stretching/dilation operator for quantum mechanics
As a counterpart to the quantum mechanical translation operator (see for example this post) is there a unitary operator which describes the stretching/dilation of a line. That is consider I have a ...
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