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)
where dX...
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...
Homework Statement
We have a vector X^a (n.b ^ indicates superscript) and covector Aa. We need to show that
X^b (d(Aa)/d(x^b) - d(Ab)/d(x^a))
transforms correctly under an artbitrary smooth change of coords. N.b the derivatives are partial.
By using the transformation rules for the...
This equation gives us (delta (rho))/rho (which I understand is the fractional perturbation in the energy density), at the time of "horizon entry" (which I'm unsure about). Does this mean the time that decoupling occured?
I'm a British student considering doing a Phd in America. If I do a Phd in England it should only take 3 years, but I've heard that usually American Phd's take a lot longer (e.g six years +). However I suspect that this may be because the typical American student is much less advanced when...
We need to show that using the Schwarzchild metric, an incoming radial spacelike geodesic satisfies r>= 1m/(1 + E^2)
I know that E = (1-2m/r) is constant, and I think that ds squared should be negative for a spacelike geodesic. I try substituting E into the metric and setting ds squared <=0...
Is it always true that dt/ds is always positive, where t is the coordinate time and s is the proper time? I suspect his is the case, but am not sure why.
"Under what conditions does a geodesic represent a possible wordline for a particle in free fall, parametrized by proper time."
I can only think of one conditions - the fact that the metric ds squared is positive. Is this enough?
I suspect that there will be more jobs available in theoretical condensed matter.
ps do theorists just work in academic institutions (and therefore have to do teaching), or can you get research jobs in companies, and just do research all the time?
I'm starting an MSc in theoretical physics this October, and at the moment I'm considering specialising in Condensed Matter or Particle Physics, both of which look quite interesting. I was wondering which one had better career prospects. I suspect it's easier to get a well paid research job in...
I start from the defintion of H, and then plug in that p is the partial derivative of L wrt q dot.
The next stage is a bit iffy. I assume that the Kinetic energy can be assumed to be 1/2 m * ((q dot) squared), where q is the position vector. I argue that any other velocity dependent terms in...
Homework Statement
Two equal masses are connected by two massless springs of constant k and nat. length l. The masses are constrained by a frictionless tube on a pivot, (also massless) so that they remain colinear with the pivot. The pivot subtends angle theta with the vertical. The 1st mass...
I'm doing a theory project on Cosmological inflation, and I've been given an equation which involves T3 which is "the effective tension of the D3 brane". I think that this is probably a numerical constant, but it's not clear from the context. If it is a constant, how could I find out the...