All Questions
5
questions
6
votes
1
answer
78
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How do I formulate a quantum version of Hamiltonian flow/symplectomorphisms in phase space to have a "geometric", quantum version of Noether's theorem
I'm currently exploring how Noether's theorem is formulated in the Hamiltonian formalism. I've found that canonical transformations which conserve volumes in phase space, these isometric deformations ...
- 111
0
votes
4
answers
374
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Is Feynman correct when he suggests that Noether's Theorem requires quantum mechanics?
I'm reading the Feynman lectures on physics. In 52-3 he discusses how for each of the rules of symmetry there is a corresponding conservation law. I'm assuming he is referring to Noether's Theorem, ...
- 39
0
votes
0
answers
51
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Why does the conserved quantity generate the transformation in quantum mechanics? [duplicate]
If we have a lagrangian with a symmetry then we get a conserved quantity: $$Q=Q(p,q)$$ which is a function of the conjugate momentum and the coordinates.
If we move over to quantum mechanics then we ...
- 1,933
3
votes
0
answers
767
views
How are the infinitesimal generators of translation related to the Lagrangian?
In studying analytical mechanics (or it's quantum analog), one will come across statements such as:
$$f(x^{i}+\delta x^{i})=f(x^{i})+\delta f(x^{i})=f(x^{i})+\frac{\partial f(x^{i})}{\delta x^{i}}\...
- 2,847
27
votes
2
answers
6k
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Why does the classical Noether charge become the quantum symmetry generator?
It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
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