All Questions
4
questions
0
votes
1
answer
210
views
Vector Laplacian in Curved Spaces
The vector gradient, $\mathbb{L}$, is defined as
$$
(\mathbb{L} W)^{ij} \equiv \nabla^{i} W^{j} + \nabla^{j} W^{i} - \frac{2}{3} g^{ij} \nabla_{k} W^{k} \,,
$$
where $\nabla_{i}$ is the covariant ...
- 698
0
votes
0
answers
1k
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Examples of Tensor Transformation Law
Let $T_{\mu\nu}$ be a rank $(0,2)$ tensor, $V^\mu$ a vector, and $U_\mu$ a covector. Using the definition of tensors based on the tensor transformation law, determine whether each of the following is ...
- 603
0
votes
1
answer
117
views
Tensor and Vector Notation
I'm given the tensor $X^{\mu\nu}$ and vector $V^\mu$ of the form
$$X^{\mu\nu} = \begin{bmatrix}
2 & 0 & 1 & -1 \\
-1 & 0 & 3 & 2 \\
-1 & 1 & 0 & 0 \\
...
- 603
1
vote
1
answer
184
views
basic vector being hermitian
If the space has a mixed metric signature, not all the basis vectors are Hermitian.
Nevertheless, they are defined to be self-adjoint under reversion. The vector transpose
conjugate is, therefore, ...
- 905