The g_ij as potentials for the gravitational field

In summary: This is the gauge invariance of general relativity. So the question is: What is the corresponding physical significance of the gauge symmetry in Einstein's field equations? The answer in Einstein's own words is: The generality of the field equations is then only apparent; the coordinate system completely determines the state of the gravitational field... the field equations are only valid with respect to a coordinate system and not with respect to arbitrary transformations. So I believe the central issue is to determine the gravitational force field in a way that is independent of the chosen coordinate system. The way out of this impasse is to give up on the idea of a gravitational force field and to embrace the idea
  • #106
It follows from the representation of the central extension of the covering group of the classical Galilei group how the wave function transforms. I have worked out once the representation theory for the Galilei group as lecture notes for a QM2 lecture. It's, however, in German (the quantum theoretical part starts with Sect. 2.5):

https://itp.uni-frankfurt.de/~hees/publ/hqm.pdf
 
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  • #107
vanhees71 said:
It follows from the representation of the central extension of the covering group of the classical Galilei group how the wave function transforms. I have worked out once the representation theory for the Galilei group as lecture notes for a QM2 lecture. It's, however, in German (the quantum theoretical part starts with Sect. 2.5):

https://itp.uni-frankfurt.de/~hees/publ/hqm.pdf

Kein problem, toll ja! Vielen dank! Ich werde es bald mal ansehen! :P

(That's more or less all the German that's left from attending 6 years German as a high-school subject)

Can you point to the page where you transform the Schrodinger equation under boosts and derive the transformation of the wave function?
 
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  • #108
This is on p. 87-88.
 
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  • #109
haushofer said:
Of course you can.

We've been round and round about this before, and you admit your viewpoint is not mainstream, and it's off topic for this thread anyway, and the OP is long gone.

I think this thread can be closed.
 

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