Questions tagged [lorentz-transformation]
The lorentz-transformation tag has no usage guidance.
9 questions with no upvoted or accepted answers
3
votes
1
answer
77
views
Practical question related to reference frames in general relativity
Sorry if my question requires clarification. I am having trouble conveying exactly what my problem is.
I'm trying to code a ray tracer that works in curved spacetime. In principle, this just entails ...
- 437
2
votes
1
answer
64
views
Relativistic time transformation in a rotating reference frame
I'm working to better understand Lorentz transformations, and it was suggested that a good exercise would be to derive the relativistically correct transformation laws from a stationary reference ...
- 1,978
1
vote
1
answer
55
views
Definition of 'proper lorentz transformation' being having positive determinant or preserving the orientation of spatial axes
In the book I am reading, the proper Lorentz transformations are defined as Lorentz transformations (hereinafter LT) with $\det \Lambda =1$. It states that:
The proper Lorentz transformations ...
- 331
1
vote
0
answers
31
views
Equation of Motion after Boost
In paper of analyticity and positivity constraints, they take example of effective field of Goldstone boson in a linear sigma model,
$$\mathcal{L}_{\text{eff}} = (\partial{\pi})^2 + \frac{c_3}{\Lambda^...
- 938
0
votes
1
answer
59
views
Lorentz transformation on field theory using coordinate expressions not representations
This is probably a stupid question but, I want to show that a Lagrangian written in field theory is Lorentz invariant WITHOUT using the Lorentz transformation representation / generators. I know we ...
- 1
0
votes
0
answers
32
views
On the distinction between Lorentz group and proper orthochronous group via Jacobian determinants
The group $O(1,3)$ is defined as the set of matrices which are orthogonal with respect to the Minkowski metric $\eta$, i.e. those matrices $\Lambda$ satisfying
$$\Lambda^T \eta \Lambda = \eta.$$
...
- 1
0
votes
0
answers
31
views
Lorentz algebra representation
In my QFT lecture the following was derived, but I have no idea how:
We consider a scalar field : $\phi(x^\mu)$.
$\phi(x^\mu)=\phi'(x'^\mu)$
Then:
$\phi'(x'^\mu)=\phi((\Lambda^{-1})^\mu_{\ \ \nu}x'^\...
- 1,624
0
votes
1
answer
78
views
Generators and Lorentz transformations (LT)
I have been trying to understand how $SO^+(1,3)$ generators are related to LT elements.
I am confused as I don't know how many types of generators are considered.
If we consider the following ...
- 1,624
0
votes
0
answers
89
views
The Low Velocity Limit of the Electric and Magnetic Field Transformations
From the covariant formulation of electromagnetism we know that the fields transform as:
$$\vec{E}'=\gamma \vec{E}-\frac{(\gamma-1)}{u^2}(\vec{u}\cdot \vec{E})\vec{u}+\frac{\gamma}{c}[\vec{u}\times\...
