Recent content by electroweak

Ah, these must be anyons.

I answered my own question (I think). Modulo redefinition of the phases of operators, projective representations are in correspondence with central extensions (as both are built out of nontrivial algebraic 2-cocycles). For n>2, Spin(n) is a universal cover, so the phase of any of its projective...

To define spinors in QM, we consider the projective representations of SO(n) that lift to linear representations of the double cover Spin(n). Why don't we consider projective representations of Spin?

Note: for discrete G, BG is the Eilenberg-Maclane space K(G,1). Perhaps this will help with the finite case.

In Dijkgraaf and Witten's paper "Topological Gauge Theory and Group Cohomology" it is claimed that... Why are either of these statements (the Lie group case or the finite case) true?

OK, I think I am missing something very basic... When regularizing phi^3 theory in six dimensions, Srednicki comes to eq 14.30, which shows that the 1-loop contribution to the propagator diverges (the gamma function has a pole). This is good. OK. Now let d=5 (or epsilon=1). Actually, go...

Consider the height function on the image of some nice immersion of the Klein Bottle in R3. Pullback the height function by the immersion to obtain a potential on the actual Klein Bottle. Is this a Morse function? If so, I can't get it to work. If not, why isn't it?

I'm reading "Mirror Symmetry" by Hori et al. In it, they compute the cohomology groups for the sphere and the torus. I tried to do the same for the Klein bottle, and it isn't working out. Is Morse homology defined for non-orientable spaces? If not, why not? Can it be extended?

We all know that the Euler characteristic is a topological invariant. But let's suppose that we don't know this or anything else about algebraic topology for that matter. We are given only the Gauss-Bonnet theorem, which expresses the Euler characteristic in geometrical terms. In his string...

I think that, by "precise", mpkannan means "determinate". If ψ is an eigenstate to begin with, we are guaranteed that its measurement will yield a particular value (the corresponding eigenvalue). Otherwise, we can't predict with certainty the outcome of the measurement. "Precise" probably...

My apologies about the confusion, everyone. When I said "mixed state", I meant what DrClaude and kith have described: a single ket. I acknowledge that a single ket can be expanded as a superposition of eigenkets. But in doing so, classical probability is not invoked. kith puts my original...

A quantum state cannot be a simultaneous eigenfunction of position and momentum. Position eigenstates do exist, as do momentum eigenstates. You just can't be an eigenstate of both. You may take an arbitrary state and measure its position, so that it becomes (collapses into) a position...

I think you're correct that I didn't set up my experiment carefully enough. Perhaps I could have gone with some form of the double slit experiment; maybe there would also be problems here. I haven't given the physical details much thought. For the sake of argument, let's suppose that...

Quantum mechanics says that physical observables are self-adjoint operators. Is this correspondence a bijection, ie can we realize any such operator as a physical observable? There are obvious practical concerns with physically realizing certain contrived operators. But are there any...

Thanks. I ended up going with Beamer. It's exactly what I wanted, and it's simple to use.