Questions tagged [lorentz-transformation]
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83 questions
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Hermitian Properties of Generators in Infinite-Dimensional Representations of the Lorentz Group
We know that finite-dimensional representations of the Lorentz group are non-Hermitian, i.e. spinor representation generators $S^{\mu\nu}$ satisfy the relation $S^{0i\dagger}=-S^{0i}$. But for ...
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Boost generators and boost representation in $SO(3,1)$
The book "Groups, Representations and Physics" by Jones says on p.208
[...] the generators of boosts $\textbf{Y}$ are anti-Hermitian. Hence when exponentiated they produce anti-unitary ...
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Relativistic magnetism confusion: different electron drift speeds in two wires and charge density in the electron frame
Many books prove that the magnetic and electric forces are the same thing observed by two different observers of two specific frames. Many books take the example of two wires carrying same current,...
user361782
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What does "equal time commutation relations" mean in the context of Special Relativity?
I'm confused, given the equal time commutation relations in scalar field theory:
$$[\phi(\vec x,t),\pi(\vec{x}',t)]=i\hbar{\bf 1}\delta^3(\vec x -\vec{x}').$$
I thought that in special relativity, we ...
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Lorentz transformation of Dirac gamma matrices
We have the formula for gamma matrices as
\begin{equation}
S \gamma^\mu S^{-1} = \Lambda ^\mu{}_\nu \gamma^\nu .
\end{equation}
Here is the $\Lambda$ performing Lorentz transformation on the gamma ...
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Why doesn’t $(\Lambda^{-1})^{\mu}_{\,\,\nu}=\Lambda_{\nu}^{\,\,\mu}$ imply $\Lambda^{-1}=\Lambda^T$ for Lorentz boosts?
According to books and lecture notes,
$$\Lambda^{-1}=\eta^{-1}\Lambda^T\eta=\eta\Lambda^T\eta$$
which I have no problem with. Then they write this in index notation as
$$(\Lambda^{-1})^{\mu}_{\,\,\nu}=...
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Why is the Wigner rotation ambiguous when comparing composed non-collinear boosts to a single effective boost?
I am trying to understand, at a technical level, how the Wigner (Thomas) rotation arises from the composition of non-collinear Lorentz boosts, and I am encountering what appears to be an ambiguity ...
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Deriving the Lorentz transformation from invariance of spacetime hypervolume
Last night, I found an interesting way of deriving the Lorentz transformation, but I never saw that approach before. So I'm wondering if this demonstration is sound, and if it was already considered ...
- 8,117
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Index order in Einstein notation [duplicate]
I am learning about four-vectors in special relativity in my electrodynamics lecture.
We have learned that under Lorentz transformations $\Lambda$, vectors transform like
$$
x'^{\mu} = \Lambda_{~~~\nu}...
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Where are the ideals of the Lorentz algebra?
I am currently studying the Lorentz group, and I am particularly interested in learning about its Lie algebra, $\mathfrak{so}(1, 3)$ (I have learned it doesn't really matter whether we are talking ...
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Active and passive transformations of scalar field
I know that questions on this topic has been asked before, but I would like to present specifically my confusion about this topic.
Let's first start with the distinction between active and passive ...
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Weird and short question on scalars and Lorentz transformations
I've been told that a Lorentz invariant or something that goes unaffected after Lorentz transformations are scalars. Now, I never really gave too much thought into it, but I now realise... Aren't
$x,y,...
- 175
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Misunderstanding the lorentz transformation
I do understand the math part of the transformation, but I have a problem understanding why exactly there will be a "triangle" (to say it simply). Pretty much all the textbooks and videos ...
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Showing $D_\mu \Psi$ transforms as a spinor with the spin connection (Supergravity Exercise 7.25)
Exercise 7.25 in Freedman & Van Proeyen's Supergravity is the following
Show that $D_\mu \Psi$ also transforms as a spinor, namely into $\exp(− 1/4 \lambda^{ab}(x)\gamma_{ab}) D_\mu \Psi(x)$. You ...
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Why can't only time dilation alone take place in special relativity, without length contraction? [closed]
An object moving relative to an observer experiences time dilation, as stated in the theory of Special Relativity.
But suppose only time dilation occurred while lengths remained unchanged.
Wouldn’t ...
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