Dear Shyan,
what you write is not really correct. There are extremely important differences between "gauge symmetries" and true "global symmetries", the first kind is NOT a real symmetry but a redundancy as mentioned above.
Say a Hamiltonian (which correspond to energy) has a certain...
I'm also very much interested in discussing these papers, although sadly I am quite busy currently and might not be able to participate too much.
Let me add some references that might be useful. Stone et al (J. Phys. A: Math. Theor. 44 045001) has clarified certain aspects of the Kitaev...
You can take a look at the book "Braid Groups" by Kassel and Turaev, what I call colored braid group they call pure braid group. I think there is a section in the beginning where they talk about a certain configuration space and prove that its fundamental group is the pure braid group, its...
I don't think I know anything simple to read, most references I know are advances math books in knot theory, quantum groups or modular tensor categories. But reading about the usual braid group (the references I gave above), is enough to understand the basics on the colored braid group...
Yes, it is what I am talking about. The article only discusses the case of two particles, in that case it is actually possible to draw simple pictures and see intuitively what the difference is between two and three dimensions for distinguishable particles. I can see if I can find a good, simple...
In two dimensions, multi-particle states (wavefunctions) has to transform as a representation of the Braid group B_N. There are infinitely many one-dimensional representations given by an angle \theta, such that the wave function changes by a phase \psi \rightarrow e^{i\theta}\psi after exchange...
Yes, non-identical particles are distinguishable. But I think "complement"'s question is why distinguishable particles have non-trivial exchange statistics while they don't have in 3D and in the book he was reading anyons were considered to be indistinguishable.
The answer is (expressed more...
In three dimensions, exchange between distinguishable particles (say of different spin or mass) are trivial but for indistinguishable ones there are fermions and bosons (forgetting para-statistics for now).
In two dimensions there are non-trivial exchange statistics both for distinguishable...
Actually, your definition of Gauge theory is not correct
For example any relativistic field theory is invariant under the Lorentz group, but not necessarily a gauge theory. Gauge theories are field theories which are invariant under local transformations, meaning that the transformation is a...
Maybe I'm the confused one, but I don't think there are any gauge symmetry (redundancy) in the Kepler problem and therefore no gauge-fixing is required. All configurations related by a SO(3) transformation are physically distinct and not "gauge-equivalent".
Anyhow, samuelr85 got the point so no...
Tom.stoer,
aren't you confusing physical symmetry (like SO(3) symmetry in the Kepler problem which is, global and physical) and gauge invariance (which is mostly local and always a reduncancy in the description of the problem). I think the Kepler example is a bad example of gauge fixing...
This doesn't make any sense, since a Chern number is a precisely defined mathematical quantity and that does not require a "physical proof" (whatever that means). And math requires that the Chern number must be an integer (because it comes from a integer cohomology).
What you probably meant...