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1 vote

Trying to understand a visualization of contravariant and covariant bases

Given the matrix of dot products between basis vectors $$A = \begin{bmatrix}\mathbf e_1 \cdot \mathbf e_1 & \mathbf e_1 \cdot \mathbf e_2 \\ \mathbf e_2 \cdot \mathbf e_1 & \mathbf e_2 \cdot \...
Antoni Parellada's user avatar
2 votes

What happens if we differentiate spacetime with respect to time?

I think what you're reaching for is the four vector velocity of an object. That is, differentiating it's position with respect to time. You started with a four dimensional vector (position) and ...
StephenG - Help Ukraine's user avatar
2 votes

Physical intuition for the Minkowski space?

I don’t think that people can give you intuition. Intuition is something that you develop through experience. Since we basically live non-relativistic lives, such experience is gained through working ...
Dale's user avatar
  • 103k
3 votes
Accepted

Why is the tensor product not a multilinear application?

The tensor product map $$\otimes : V_1\times \cdots\times V_n \to V_1\otimes \cdots \otimes V_n$$ is multi linear as the codomain is a linear space and the map is separately linear in each entry. ...
Valter Moretti's user avatar
0 votes

Why is the $\theta$ term of QCD violating charge and parity (CP) symmetries?

Old post, but I just heard of the following analogy recently so I thought I'd share. In the comments and elsewhere on this site, people have given a good answer about the mathematical answer to why ...
11zaq's user avatar
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0 votes

What is the advantage of using spherical tensor over cartesian tensor?

The Cartesian tensor is just $3\times 3=9$ values tied to an arbitrary coordinate system, and they get scrambled by rotations. While as you point out, spherical tensors are irreducible, and that means:...
JEB's user avatar
  • 35.3k
0 votes

What is the advantage of using spherical tensor over cartesian tensor?

The Coulomb potential is spherically symmetric. As a consequence, the wave functions of electrons orbiting a nucleus contain spherical harmonics. Therefore it is better to work in a spherical basis.
Jesse's user avatar
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