# Recent content by andrey21

1. ### Transformation from Cartesian to spherical polar coordinates

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...
2. ### Pauli-Lubanski pseudovector

So I have the correct answer, thats great. Thanks for all your help :smile:
3. ### Pauli-Lubanski pseudovector

I understand so you end up with: W2= -(J10P3+J30P1+J31P0) Correct?
4. ### Pauli-Lubanski pseudovector

So using that information and that: ε1234=1 and ε1243=-1 W2= -1/2 (-J10P3+ J30P1+J10P3 +J31P0-J30P1-J31P0) =-1/2 (0)
5. ### Pauli-Lubanski pseudovector

:rofl: Thats what I meant... So M31= - M13 for example...
6. ### Pauli-Lubanski pseudovector

OK so the antisymmetry rule again is: Mab=M-ab
7. ### Pauli-Lubanski pseudovector

OK so the other four terms would be: ε2301 M30P1 ε2310 M31P0 ε2130 M13P0 ε2103 M10P3
8. ### Pauli-Lubanski pseudovector

Ok Im a little confused, could you go into more detail regarding your expansion? Im struggling to see how you got those terms! :confused:
9. ### Pauli-Lubanski pseudovector

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
10. ### Pauli-Lubanski pseudovector

Ive tried the method mentioned in the post below: https://www.physicsforums.com/showthread.php?t=245130
11. ### Pauli-Lubanski pseudovector

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
12. ### Differential coefficients & metric tensor (Urgent)

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...
13. ### Consider the vector Vμ(3,1)

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
14. ### Transformation from Cartesian to spherical polar coordinates

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...
15. ### Consider the vector Vμ(3,1)

Using the fact that: gμv= 2x2 identity matrix and the dot product is given by: VμVμ=gμv VμVv Therefore: Vμ=gμvVv So is it correct to say: Vμ= (3,1)