You can find some relevant information in :
Group theory and its application to physical problems
Par Morton Hamermesh
The last update :
The Mathematical Theory of Symmetry in Solids: Representation Theory for point groups and space groups
by Christopher Bradley,Arthur Cracknell
Use the generalization of the differential operators in n-dimensions.
e.g. http://en.wikipedia.org/wiki/Gradient
A clue of what happens there can be found in wiki for this kind of higher dimensional gepmetry :
http://en.wikipedia.org/wiki/Hypersphere
If you have spherical invariance...
If you have :
d X/dt = AX where A is a diagonalisable matrix and X a column vector.
U^-1AU=D where D is the diagonal matrix : diag(lambda_1...lambda_n)
d X/dt = AX <=>
d X/dt = UDU^-1X <=>
U^-1dX/dt = DU^-1X <=>
dY/dt = D Y with Y =U^-1X provided that A is time independant. The mixing comes...
I would rather say that the Higgs boson is the elementary particle (that creates a lot of problem in the SM such as triviality, naturalness, etc...) and the Higgs mechamisn is the possibility of having a scalar condensate that spontaneously breaks SU(2)*U(1) -> U(1). In this sense, a top quark...
I would say the same as the others. I had a student that turned 35 during his training period of MSc in Theoretical Physics after being high school-teacher in an irrelevant field for years (needs less than BA).
It's more than doable, it's a good idea. Actually, you will probably give new...
Well actually for effective theory considerations, there are actually two "schools".
There are people trying to use perturbation theory at any cost and using mainly power-counting arguments. Which seems to be what Burgess does. Let me note by the way what Georgi (a very smart guy) told to...
Well, I wouldn't say that from what the paper says it is obvious ... From my point of view the proof for this has to be constructive. You will probably find one in Zinn Justin book or in Itzykson's. For more pedagogical aspects I would say : Abers and Lee Physics Reports on gauge theories and...
I think we have a misunderstanding here. When I discuss Wilson's ideas, I mean what is now called Functional Renormalization Group. For this, there are mainly 3 schemes : Polchinski's relying on the functional W and a smooth cut-off function, Wegner-Houghton and the shapr cutoff and average...
This is the perturbative way of seeing stuff... The only purpose of such a process is to get rid of the physics you don't know (i.e. the UV). You reparametrize everything in the IR with the IR couplings and degrees of freedom. Perturbation theory moves the UV cut-off (up to infinity at the end)...
Hello
I would say that actually you described two different things :
- Sending the cut-off to infinity is usually done in high-energy physics because you don't know where it stands actually. Sending it to infinity and keeping finite part provides you the asymptotic behaviour in a sense ...
(a) it is a transformation that rexpresses your physical situation in terms of lower energy degrees of freedom but keeping the same physical content. It is related to a change of observation scale (always from microscopic to macroscopic situation, in this sense it is a semi-group)
(b) a fixed...
Hello !
I am new on the forum but I will try to help as i can.
The case a=1 tells you in that case that the Kernel has dimension n-1 (only one free direction given by column vector with only 1 in it). So that you now that the determinant has to include (a-1)^(n-1). You just miss the last...