Could we list examples of symmetries that preserve only the combination of the measure $\mathcal{D}\phi$ together with $e^{-S}$ but not each on their own? (That is, symmetries which have no classical analogue).
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I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$ \psi = A e^{-\beta r} $$ with $A = \frac{\bet...
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I want to know what happens to the space a black hole crosses over as our galaxy travels through space.
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