All Questions
108
questions
1
vote
1
answer
144
views
Physical intuition for the Minkowski space?
As the title suggests, I am looking for physical intuition to better understand the Minkowski metric.
My original motivation is trying to understand the necessity for distinguishing between co-variant ...
- 11
0
votes
1
answer
51
views
Trouble understanding tensor notation for relativistic transformations
For $x^\mu$ with $\mu_0=t, \mu_i = x^i$ and $\eta_{\mu v}$ the metric tensor with diagonal $(-1,1,1,1)$ and zeros elsewhere, the condition for equivalence of inertial frames is stated as for some &...
- 143
3
votes
0
answers
68
views
Counting independent components of Lorentz tensor
Say I have Lorentz tensors $A^{\mu\nu}$ and say this Lorentz tensor is symmetric under $\mu \Leftrightarrow \nu$ and there are only $p^\mu$ and $q^\mu$ as the physical Lorentz vectors involved. If so, ...
- 857
3
votes
2
answers
408
views
Self-studying GR. Stuck on Q3.20 in the 3rd edition of Schultz. Orthogonal coordinate transforms in Euclidian space
I am self-studying GR using "A first course in general relativity, 3rd edition". I'm doing my best to be diligent and work though the problems at the end of the chapter. But question 3.20 ...
- 33
-4
votes
1
answer
66
views
Cannot understand this identity between kronecker and metric tensor [closed]
I'm working on Lorentz generators and I am really not able to understand this relation:
$$\omega_{\rho \sigma} \eta^{\rho\mu} \delta^{\alpha}_{\nu} = \frac{1}{2}\omega_{\rho \sigma} \left(\eta^{\rho\...
- 361
1
vote
1
answer
91
views
Questions about Lorentz Matrices and Lorentz Metric
(I use the abstract index notation convention in this post)
In $\mathbb{R}^4$, denote the Lorentz Metric as $g_{\mu\nu}=$diag$(-1,1,1,1)$, then we can define the Lorentz Matrices to be all $4\times 4$ ...
- 77
0
votes
1
answer
69
views
Doubt about product of four-vectors and Minkowski metric [closed]
Given the Minkowski metric $\eta_{\mu\nu}$
And $\eta^{\mu\nu}\eta_{\mu\nu}$=4
I can write $\eta^{\mu\nu}\eta_{\mu\nu}k^{\mu}k^{\nu}$=$4k^{\mu}k^{\nu}$
But $\eta^{\mu\nu}\eta_{\mu\nu}k^{\mu}k^{\nu}$=$\...
- 13
-1
votes
2
answers
95
views
Confusion with Lorentz indices notation
Apologies in advance if this question has been asked before (if it has, I can't find it).
I am really confused with the right-left index notation of the Lorentz matrix.
In the very first exercise of ...
- 280
0
votes
0
answers
432
views
How to know if a matrix is a (0,2) tensor, a (2,0) tensor or a (1,1) tensor?
For example:
$$
X = \begin{bmatrix}
1 & -1 & 0 & 0 \\
-1 & 0 & 5 & 3 \\
-2 & 1 & 0 & 0 \\
0 & 1 & 0 & 2
...
- 157
1
vote
1
answer
516
views
Contraction of Levi-Civita tensor in Minkowski space-time (or any space-time)
I know that $\varepsilon_{i_1 i_2\cdots i_n}\varepsilon^{i_1 i_2\cdots i_n} = n!$ in Euclid space.
But in Minkowski space-time, the metric tensor is:
$$
\eta_{\mu\nu} = \mathrm{diag}\{-1, 1, 1, 1\}
$$
...
- 157
1
vote
1
answer
87
views
Electromagnetic tensor and its components
I'm dealing with the covariant formulation of electromagnetism and I've come across the Electromagnetic tensor after learning a bit about the covariant notation.
In particular I've problems ...
1
vote
3
answers
636
views
Difference between upper and lower indices in Einstein notation
Consider a $(2,0)$ tensor $X^{\mu \nu}$ that can be represented in matrix form by:
$$X^{\mu \nu} =
\pmatrix{
a & b & c & d \\
e & f & g & h \\
i & j & k & l \\
m &...
- 337
0
votes
1
answer
63
views
How to convert the following Matrix equation to tensor notation?
Consider the following equation :
$$\Lambda^{-1}\Lambda^T \Lambda=A$$
Here $\Lambda$ are my lorentz transformations such that $\Lambda^T \eta \Lambda=\eta$. $A$ is some matrix.
I know that in terms of ...
- 1,791
3
votes
2
answers
193
views
Problem with proving the invariance of dot product of two four vectors
I am having a spot of trouble with index manipulation (its not that I am very unfamiliar with this, but I keep losing touch). This is from an electrodynamics course - we're just getting started with 4 ...
- 322
0
votes
1
answer
59
views
Not so trivial indeces in isometries of special relativity
I am trying to understand isometries and how to work with tensors.
I know that in special relativity metric transforms as follows
$$
g_{\alpha^{\prime} \beta^{\prime}}=g_{\alpha \beta} \Lambda_{\...
