Just like to pick up in this old thread, still having trouble with the question.
Using what I have already done:
δrθ=(∂r/∂x . ∂x/∂θ) + (∂r/∂y . ∂y/∂θ) + (∂r/∂z . ∂z/∂θ) (1)
Where:
x=r sin θ cos φ and y= r sin θ sin φ z= r cos θ
Would (1) then become:
δyx= = ((sin...
Well here is my answer:
W2= 0.5 M\mu\nu M\mu\nu P2 + M\mu\rho M\nu\rho P\mu P\nu
Where the Pauli-Lubanski pseudovector given was:
Wμ= - 0.5 \epsilon\mu\nu\rho\sigma J\nu\rho P\sigma
Hi can anyone help me prove the result of W2 of the Pauli-Lubanski pseudovector :
This is very new to me and I've read I must use terms such as J13 and P3
Where totally antisymmetric symbol is defined by:
\epsilon1234=1 and \epsilon1243=-1
Consider a flat 2-dimensional plane. This can be described by standard Cartesian coordinates (x,y). We establish a oblique set of axes labelled p and q. p coincides with x but q is at an angle θ to the x-axis.
At any point A has unambiguous co-ordinates (x,y) in the Cartesian system. In...
Im told to consider the specific example of the vector:
Vμ = (3,1) in the Cartesian coordinates.
gμv is the metric tensor
Yes I believe they are bases, the question is based around raising and lowering the index in tensors
Transformation from Cartesian to spherical polar coordinates
In dimensions:
x=r sinθ cos \varphi and y= r sin θ sin \varphi z=r cos θ
Show one example of:
∂z\alpha/ ∂xμ . ∂xμ/ ∂z\alpha = δ\alpha\beta
Now here is my answer:
δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂\varphi...