All Questions
18
questions
0
votes
2
answers
254
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Why is Lorentz Transformation defined with one super and one sub index?
I came across the Lorentz transformation in tensor form, usually written as
$$\Lambda ^\mu _{\nu}$$
I understand that the first index usually corresponds to rows and the second to columns, and while I ...
- 538
2
votes
1
answer
116
views
Contravariant Components (Susskind's book)
In his book about SR & classical field theory, Susskind generalizes from the differential of $X'$ (function differential) to any 4-vector. I got stuck there trying to figure out why it is ...
- 21
0
votes
1
answer
65
views
Fraction with components of Lorentz transformation
I want to show how partial derivative transforms under a Lorentz transformation.
Since the partial derivative has a fixed definition with respect to the $x$-coordinate it stays unchanged: $\partial_\...
- 425
0
votes
2
answers
53
views
Are these two "notations" the same? [closed]
Say we have a tensor $T^{\sigma\tau}$ and I want to now how it transforms, the transformation coefficients in terms of Lorentz transformation matrices would be: $$T^{\mu'\nu '} = L^{\mu '}{}_{\sigma}L^...
- 11
4
votes
2
answers
851
views
Lorentz transform of Levi-Civita Symbol
I was reading about Lorentz transformations and frequently I hear the notion of Lorentz transforming quantities like $\epsilon^{\mu \nu \rho \sigma}$. But I have never heard an explanation as to why ...
- 149
1
vote
0
answers
36
views
Completely antisymmetric unit tensor of fourth rank in different 4D coordinate systems [duplicate]
I am reading Landau's Classical Theory of Fields. On page 18, it is said that the completely antisymmetric unit tensor of fourth rank $\varepsilon^{iklm}$ is defined as the same in all coordinate ...
- 613
7
votes
6
answers
830
views
Deriving $\Lambda^i_{\,j}$ components of the Lorentz transformation matrix
I am trying to follow Weinberg's derivation (in the book Gravitation and Cosmology) of the Lorentz transformation or boost along arbitrary direction. I am having trouble deriving the $\Lambda^i_{\,j}$ ...
- 682
1
vote
3
answers
150
views
Still confuse about tensor
In special relativity, a four-vector $\mathbf{x}$ in an inertial frame is related to $\mathbf{\overline{x}}$ through a Lorentz transformation $\mathbf{\Lambda}$:
\begin{align}
\overline{\mathbf{x}}...
- 1,083
2
votes
3
answers
85
views
Can I contract index in this expression?
I'm reading Carrol text on general relativity, on page 96 they arrive to the term
\begin{equation}
\frac{\partial x^{\mu}}{\partial x^{\mu '}}\frac{\partial x^{\lambda}}{\partial x^{\lambda '}}\frac{\...
2
votes
2
answers
1k
views
How to determine if a tensor is covariant or contravariant?
In special relativity, the coordenates of a event are in general written using a 4-vector: $$x^{\mu} = \binom{ct}{\textbf{x}}$$ where $\textbf{x} = (x,y,z)$ are the spacial coordenates. This is a ...
- 587
0
votes
0
answers
375
views
The chain rule and velocity transformation in relativity (2)
First of all, these answers (How to derive the law of velocity transformation using chain rule?, The chain rule and velocity transformation in relativity, and other from a quick search on this site.) ...
- 3,085
0
votes
1
answer
48
views
Computing the metric in the barred frame using a 2D coordinate transformation
I would like to apply the coordinate transformation $x^{\bar{1}} = 2x^1$, $x^{\bar{2}} = x^2$ in the 2D Cartesian plane. The metric in the barred frame is $g_{\overline{ij}} = \Lambda^i_{\bar{i}} \...
- 259
0
votes
4
answers
268
views
A fundamental question about tensors and vectors [closed]
Studying relativity, I am deeply confused with the fundamental concept of vectors and tensors. Are they some specific "realities" that "exist" independently of coordinates? If so, given a vector $\...
- 1,669
2
votes
4
answers
673
views
Use of the Kronecker Delta in Translations
A translation in special relativity is, as I understand, a kind of Lorentz transformation given by:
$x^{\mu} \rightarrow \delta^{\mu'}_{\mu}(x^{\mu} + a^{\mu})$ where $ \delta^{\mu'}_{\mu} = 1$ if ...
- 301
5
votes
1
answer
711
views
Antisymmetric tensor and pseudotensor
I am reading Landau & Lifshitz's classical field theory book, and there is a paragraph which confused me:
"With respect to rotations of the coordinate system, the quantities $e^{iklm}$ behave ...
- 670