Loosely-threaded thoughts [mostly] about mathematics and physics.

Why is momentum the generator of translations?

In quantum mechanics, it is often stated that the momentum [operator] is the generator of translations. However, most texts fail to give a satisfactory justification to this claim, if any is given at all. What we will do here is define precisely what it means for observable to be a generator of a group of transformations, both in quantum and cla...

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