Timeline for The measure on the harmonic spectrum from Selberg trace formula
Current License: CC BY-SA 3.0
8 events
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| Aug 13, 2013 at 14:32 | comment | added | user6818 | So what is the choice of normalization that is being maintained here? I am not seeing what would have been lost if they just had $\pi \lambda tanh(\pi \lambda)$? | |
| Aug 13, 2013 at 13:42 | comment | added | Marc Palm | No, this factor in the physics paper is not a volume. To call it volume is confusing. The volume of $\mathbb{H}$ is infinite. The authors simply encode the chosen normalization of the Plancherel measure in "vol(H^2)". | |
| Aug 13, 2013 at 13:27 | comment | added | user6818 | Even in their references I never see this curious Vol(H^2)/(4\pi) factor - that is totally mysterious. [...thats why I remembered the Selberg trace formula since it produces similar prefactors..] | |
| Aug 13, 2013 at 13:11 | comment | added | Marc Palm | theoretic perspective. For a purely analytic proof, I am the wrong person to ask. | |
| Aug 13, 2013 at 13:06 | comment | added | Marc Palm | The article suggest further references. I has nothing to do with the trace formula for sure, but only with the Plancherel measure which enters into the trace formula only as one ingredient. The translation between irreducible representations goes as follows. You only restrict to unitary irreducible representation of SL(2,R) with $SO(2)$-invariant vectors. Those are called spherical. You obtain principal series representation. The complementary series representation don't turn up. Their $SO(2)$-invariant vectors correspond to eigenfunctions of the Laplacian. This is the representation... | |
| Aug 13, 2013 at 13:02 | comment | added | user6818 | So can you explain how the equations 3.19 and 3.20 can be derived? (independently of the Selberg trace formula?) I have seen a derivation of the spectral measure of the upper half plane being $\pi \lambda tanh(\pi \lambda)$ but $3.19$ is not really that and hence I am wondering where the difference comes from... | |
| Aug 13, 2013 at 12:56 | history | edited | Marc Palm | CC BY-SA 3.0 |
added 80 characters in body
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| Aug 13, 2013 at 12:46 | history | answered | Marc Palm | CC BY-SA 3.0 |