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accepted Dirac operator in curved spacetime in 2 dimensions – hermitian?
Feb
28
comment Dirac operator in curved spacetime in 2 dimensions – hermitian?
@HydroGuy: Ooh, I like that way of putting it. It's not entirely obvious that being real on all fields $ψ$ is equivalent to the operator being hermitian, but if I remember correctly, that is true in complex Hilbert spaces.
Feb
27
comment Dirac operator in curved spacetime in 2 dimensions – hermitian?
Thanks, but could you expand on why the Lagrangian has to be hermitian? For instance, I get that the Hamiltonian has to be hermitian, so the potential energy of the Lagrangian should be of the form $-\psi^{\dagger}H\psi$ with $H$ a hermitian operator. What about the time derivatives, though? Also, you say "pseudo-hermitian" due to the fact that $\overline{\psi}$ differs from the adjoint $\psi^\dagger$ by the matrix $\gamma^0$?
Feb
19
asked Dirac operator in curved spacetime in 2 dimensions – hermitian?
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9
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3
comment Theory behind patterns formed on Chladni plates?
Actually, Chladni plates are not described by the wave equation, i.e. by the eigenfunctions of the Laplacian, but by the eigenfunctions of the biharmonic operator, i.e. the Laplacian squared. More information and historical references can be found in a beautiful article by Gander and Wanner. Even if you try to derive the wave equation for a string, using the "masses connected by strings" model, you have to assume that it is under tension, i.e. the springs are pre-stretched, or you will get the biharmonic operator and not the wave equation.
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accepted Propagator for Dirac equation in real space
Feb
7
answered Propagator for Dirac equation in real space
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reviewed Edit Why does ice form on bridges even if the temperature is above freezing?
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29
revised Why does ice form on bridges even if the temperature is above freezing?
Adding more tags (but no "ice" tag)
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