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seen Feb 18 '11 at 21:43

Feb
18
accepted Dirac equation on general geometries?
Feb
18
comment Dirac equation on general geometries?
Very cool. I've seen something similar for C60, but in that case they just assume a spherical geometry (no fun). This looks like a nice lead. Thanks!
Feb
18
comment Dirac equation on general geometries?
Sounds like fun, but if you're considering particles with a given chirality I think you're out of luck because you can't define Weyl spinors on a nonorientable surface. In other words, I believe it's impossible to consistently use each fiber of a nonorientable bundle as a representation space for the spin group (i.e., it has no spin structures). (Not taking any points off though!!)
Feb
18
revised Dirac equation on general geometries?
edited body
Feb
17
awarded  Editor
Feb
17
revised Dirac equation on general geometries?
added 397 characters in body
Feb
17
asked Dirac equation on general geometries?
Jan
25
awarded  Scholar
Jan
25
accepted Separation of variables, eigenfunctions of the Dirac operator
Dec
2
comment Separation of variables, eigenfunctions of the Dirac operator
"Typically, the approach is to solve this using the Schrödinger equation, and then treat the spin-orbit coupling as a small perturbation on top of that" Yes, I've come across this approach as well and suspect it's the "right" thing to do in practice, but since my interest is in understanding the connection with geometry I'm willing to consider less practical stuff. ;)
Dec
2
comment Separation of variables, eigenfunctions of the Dirac operator
Done. I guess I added the tag because I saw the Lorentz group coming up a lot in this context... and because I'm not a physicist! ;)
Dec
2
revised Separation of variables, eigenfunctions of the Dirac operator
edited tags
Dec
2
comment Separation of variables, eigenfunctions of the Dirac operator
I'm ok with this; I think the irreducible representations you're considering (the Weyl spinors?) correspond to what I'd call even and odd functions (i.e., functions taking values in the even or odd part of the Clifford algebra, resp.). And the spinor Dirac operator maps from even to odd and vice versa. I'm trying to understand the physical meaning though: what do these even and odd parts correspond to? You mentioned chirality -- does chirality have a physical meaning here? Maybe that would help explain why one wouldn't want to consider eigenvectors of mixed chirality.
Dec
2
awarded  Student
Dec
2
asked Separation of variables, eigenfunctions of the Dirac operator