Monday, February 16, 2009

The search for the Higgs boson

A babyish, physicky explanation, versus the real McCoy.
Posted by at
Labels: , , , ,

6 comments:

Mr roT said...

The real thing has something called a "gerbe". This is what big-time flying-around-to-conferences-and-acting-important mathematics has come to. Time to buy a vacuum pump and move to Idaho to keep Drew Gilpin Faust's gil-pin out yer butt in academia.

2/17/2009 12:06 AM
Tecumseh said...

Even after reading the definition, I still don't know what a gerbe is. But hey, There is clearly a larger picture here: unitary gerbes take their place in a hierarchy, beginning with functions to the circle, then principal circle bundles, then gerbes and next 2-gerbes, and so on. The circle of life. Get it?

2/17/2009 12:36 AM
Tecumseh said...

Actually, reading through Hitchin's piece (he writes very well), this crazy notion is starting to make some kind of sense:

The best-known example of a gerbe with connection arises when the manifold M is a compact simple Lie group G. There is a natural gerbe on G whose curvature is a multiple of the bi-invariant 3-form B(X, [Y,Z]) , where B is the Killing form—for G = U(n) this is tr(g−1dg)3 . Whereas a line bundle has holonomy around a closed curve, a
gerbe has holonomy around a closed surface. More
generally, if the curvature of the gerbe vanishes,
then there is holonomy in H2(M,U(1)).

OK, what's so bad about that?

This approach forms the basis of the active area
of twisted K-theory. To a bundle of projective
Hilbert spaces one can associate a bundle of Fredholm operators Fred(P), since the scalars act trivially by conjugation and the twisted K-group
KP (M) is defined to be the space of homotopy
classes of sections of Fred(P) → M.

Powwww, Mr Rot!! Can Dolbeault cohomology be too far away?

2/17/2009 12:48 AM
Mr roT said...

Gerbe is Felchmath. Ask AA.

2/17/2009 3:22 AM
Pepe le Pew said...

then there is holonomy in H2(M,U(1)).

homospeak

2/17/2009 4:38 AM
Mr roT said...

Pepe, exactly. Astronomy is the system of laws governing astroglide. Same with hole onomy.

2/17/2009 10:26 AM

Post a Comment

Subscribe to: Post Comments (Atom)