All Questions
33
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
71
views
On covariant form of Lorentz equation
The non-relativistic version of Lorentz equation has the form
$$m\frac{d\vec{v}}{dt}=q(\vec{E}+\vec{v}\times\vec{B}) $$
Where $\vec{v}, \vec{E}, \vec{B}$ refers to the velocity of charged particle, ...
- 1,752
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
2
votes
1
answer
110
views
Four-vector and Notation significance [closed]
As the title suggest, this has to do, on the most part, with four vector notation. I have a series of questions, the majority, related to this topic:
1- If we assume a lorentz boost in the x direction ...
- 1,398
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
2
votes
1
answer
171
views
Why not define tensors under Galilean or Poincare transformations?
I have seen vectors (and tensors, in general) defined under rotations,
$$V^i=R^i_{~j}V^j$$
and under Lorentz transformations,
$$V^{\prime\mu}=\Lambda^\mu_{~~\nu}V^\nu$$
where $R,\Lambda$ are the ...
- 11.8k
1
vote
1
answer
219
views
How to contract spinor indices?
In normal vector representation, vectors can be contracted as follows:
$$v^\mu v_\mu$$
with one covariant and one contravariant index. But in spinor representation, there are 4 possible type of ...
- 1,324
0
votes
1
answer
486
views
Show that the contraction of a covector and a vector is Lorentz invariant
I just got Sean Carroll's Spacetime and Geometry: An Introduction to General Relativity a couple of weeks ago, and I have resolved to go through the entire book. In the first chapter, he prompts the ...
- 187
2
votes
2
answers
639
views
Trying to understand electric and magnetic fields as 4-vectors
I was trying to show that the field transformation equations do hold when considering electric and magnetic fields as 4-vectors. To start off, I obtained the temporal and spatial components of $E^{\...
user161157
4
votes
3
answers
1k
views
Showing that 4D rank-2 anti-symmetric tensor always contains a polar and axial vector
In my special relativity course the lecture notes say that in four dimensions a rank-2 anti-symmetric tensor has six independent non-zero elements which can always be written as components of 2 3-...
- 2,604
5
votes
4
answers
3k
views
Is the Four-gradient of a Scalar Field a Four-Vector?
Consider a scalar field $\phi$ as a function of spacetime coordinates $x^\mu$. The four-gradient of $\phi$ is given by
\begin{equation}
\frac{\partial \phi}{\partial x^\mu} = \left( \frac{\partial \...
- 1,290
0
votes
0
answers
211
views
What are covectors in special relativity?
In special relativity the purpose of vectors makes fairly intuitive sense, they represent a point in spacetime:
$$x^{\mu}=\begin{pmatrix}x^0 \\ x^1 \\ x^2 \\ x^3\end{pmatrix}$$
and we can define the ...
- 6,963
1
vote
3
answers
240
views
In electromagnetism, how do we know that either $F^{\mu\nu}$ or $A^\mu$ is a tensor?
In special relativity the partial derivative $\partial_\mu$ is a tensor. Now if some function $A^\mu$ was a tensor, then also the quantitiy $F^{\mu\nu}=\partial^\mu A^\nu - \partial^\nu A^\mu$ would ...
- 391
3
votes
3
answers
3k
views
How to prove a 4D vector is a 4-Vector?
This is a fairly open ended question.
Given a set of 4 Components, that is, a 4D Vector, what is the process for determining rather or not it is a "4-Vector" as defined in special relativity? I want ...
0
votes
2
answers
1k
views
How does 4-vector notation work?
In particle physics we are going over 4-vector notation. However, my background on this is a little shaky, and I'm having difficulty differentiating the notation and visualizing what it actually means....
- 795