Because any property satisfied to first order in the generators will hold for the exponent. This is a general property of all one-parameter subgroups such as those you've described. Look at the exponent this way:
e^{\lambda T}=(1+\frac{\lambda}{N}T)^{N}=(1+\delta\lambda T)^{N}
for...
Bah, of course. I remembered the number three and that it all seemed miraculous somehow. Yes, the quarks cancel the lepton anomalies. I should really start looking these things up before I type. I thought that the 45 GeV neutrino had been ruled out...
String theory does have the Higgs Mechanism, as do all field theories. You will have to learn some maths before you can really discuss it, though, unfortunately.
the winding number just counts how many times a field or object raps around a compactified dimension (a.k.a a circle). You might have a field or object that goes something like \phi (x,y)=\phi (x) e^{i2\pi n y/R}
Now let's say that y is defined modulo R, y ~ y + R (that is: the compactified...
No one can say at the moment why there Must be three, but there is good evidence that there are no more than three within the framework of basic QFT. For instance, the width of the Z boson measurement is sensitive to the number of generations, and experiments agree with only three generations...
thanks everyone for your comments. I've been persuaded to check out Mukhanov's book. I guess my original question has been answered so I will just make a few comments for clarity.
I think so. Specifically the anomalies that arise when one tries to incorporate a curved space connection into...
thanks, I actually looked at Wald's book but found the equation editor he used unbearably cryptic. My library doesn't have the "Intro..." book so I'll have to look for it elsewhere. I realize that this isn't quantum gravity, however, the equations require one to introduce a curved space...
I recently checked out Davies' and Birrell's book "Quantum fields in curved space" and I noticed that it was written in 1982. My question is, did the authors know about the anomalies and that QFT could not incorporate gravity at that time? The table of contents has nothing on anomalies. I am...
if the proton and electron are moving at sufficiently high speeds they will not form Hydrogen. This is analogous to a rocket leaving earth. It must have an escape velocity, otherwise it will remain bound to Earth's orbit. An electron with a velocity greater than the escape velocity will...