We are asked to show that L(SO(4)) = L(SU(2)) (+) L(SU(2))
where L is the Lie algebra and (+) is the direct product.
We are given the hint to consider the antisymmetric 4 by 4 matrices where each row and column has a single 1/2 or -1/2 in it.
By doing this we generate four matrices...
We have a suggested Lagrangian
epsilon(abcd) F^(ab) F^(cd)
and are asked to comment if this is a sensible EM Lagrangian. The only thing i can think of is that its still gauge invariant in the normal way but otherwise im stumped. would appreciate any suggestions. thanks
I'm studying a QFT course, and we've been asked to consider why classical physicists found it useful to introduce electric and magnetic fields, but not fields for electrons or other particles. I'm completely stumped, and would appreciate any hints. thanks
Assuming the Lorentz force law and also that in the rest frame of the particle the 3 acceleration is zero, we need to explain why the following equations hold:
E.v = 0 and E + v.B = 0
where v is the velocity.
I think this is because g(A,A) = -a squared is invariant. Therefore if a=0, I...
We have to show that [Lx,Ly] = Lz
[Ly,Lx] = -Lz
[Lx,Lx] = 0
and I have done this. We then need to comment on the significance of these results, which I'm not sure of. I know in QM you get similar results for commutators of these quantities, and it means that you can't simultaneously know...
"A parcel of air is lifted slowly from the ground, where the temperature is 295K, to an elevation of 5km, and then returned rapidly to the ground. Estimate the air parcel temperature at 5km and after it returns to the groundm explanation any assumptions."
I assumed an adiabatic process both...
We are given a form of Einstein's field equations:
3R'' = -pR
R''R + 2((R')^2) = p(R^2)
where p is a constant and R' = dR/dt
Assuimg that R and R' are both positive, we are asked to show that the general solution is R(t) = A*[(t-ti)^(2/3)]
I'm very confused about this. If we...
We have a hyperbolic pde (in fact the 1d wave equation) with indep vars X, T
We use the central difference approximations for the second derivatives wrt X, T to get
[phi(Xn, Tj+1) -2phi(Xn, Tj) + phi(Xn, Tj+1)]/(dT^2) = [c^2][phi(Xn-1, Tj) -2phi(Xn, Tj) + phi(Xn=1, Tj)]/(dX^2)
You mentioned something interesting; do departments ever grant exemption from GRE's for candidates with well recognised qualifications (for example an MSc from Cambridge or Imperial? If so, then it might be worth me contacting individual departments to see their policies.
Hi, I'm a UK student who wants to do a Phd in a year (after I finish my MSc). I'm a little bit puzzled about the status of the GRE in physics at US institutions. Looking at some webpages it seems as if the GRE is always mandatory, and that they use it as a major way of discriminating between...
I managed to get this. I was differentiating with respect to the wrong coordinate system, which messed up the calculation. I then tried using the chain rule and differentiating with respect to the other coord system and it all fell out.
"Show that if a space time metric admits three linearly independent 4 vector fields with vanishing covariant derivatives then Rabcd = 0"
We can set the three vectors as (1,0,0,0), (0,1,0,0) and (0,0,1,0). Use covariant derivative of vector field X^b is:
d(X^b)/d(x^a) + (Christoffel symbol...