All Questions
Tagged with special-relativity tensor-calculus
389
questions
4
votes
1
answer
372
views
S. Weinberg, "The Quantum theory of fields: Foundations" (1995), Eq. 2.4.8
Unfortunately I'm struggling to understand how do we get eq. (2.4.8) from eq. (2.4.7), p. 60; namely how $(\Lambda \omega \Lambda^{-1} a)_\mu P^\mu$ is transformed into $\Lambda_\mu^{\;\rho}\Lambda_\...
- 55
3
votes
0
answers
923
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The connection between classical and quantum spins
I have two questions, which are connected with each other.
The first question.
In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
user8817
7
votes
6
answers
4k
views
Why define four-vectors to be quantities that transform only like the position vector transforms?
A four-vector is defined to be a four component quantity $A^\nu$ which transforms under a Lorentz transformation as $A^{\mu'} = L_\nu^{\mu'} A^\nu$, where $L_\nu^{\mu'}$ is the Lorentz transformation ...
- 401
2
votes
1
answer
2k
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What is the Lorentz tensor with a superscript and subscript index?
I have been reading about symmetries of systems' actions, e.g. the Polyakov action, and I have encountered Lorentz transformations of the form: $\Lambda^{\mu}_{\nu} X^{\nu}$. I am moderately familiar ...
- 91
2
votes
0
answers
287
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Solving the equation of relativistic motion
How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
0
votes
1
answer
242
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Tensor manipulation
Having a bit of trouble applying what I know about tensor manipulation, given,
$T^{\mu \nu} = \left( g^{\mu \nu} - \frac{p^\mu n^\nu + p^\nu n^\mu}{p \cdot n} \right)$,
I need to compute quantities ...
- 295
0
votes
3
answers
1k
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Relativistic basic question - four vector, Lorentz matrix
I have heard relativistics only very compressed during my student time. Now I looked up the definitions again and a question comes into my mind:
A contravariant vector is transformed like this: $(a^...
- 358
24
votes
4
answers
4k
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Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?
Maxwell's equations, in differential form, are
$$\left\{\begin{align}
\vec\nabla\cdot\vec{E}&=~\rho/\epsilon_0,\\
\vec\nabla\times\vec B~&=~\mu_0\vec J+\epsilon_0\mu_0\frac{\partial\vec E}{\...
- 9,675
2
votes
1
answer
73
views
Testing covariance of an expression?
This is something I've been unsure of for a while but still don't quite get.
How does one tell whether an expression (e.g. the Dirac equation) is covariant or not? I get it for a single tensor, but ...
- 87
3
votes
2
answers
1k
views
What are $\partial_t$ and $\partial^\mu$?
I'm reading the Wikipedia page for the Dirac equation:
$\rho=\phi^*\phi\,$
......
$J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$
with the conservation of probability ...
- 203
5
votes
1
answer
544
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Confused about indices of the Ricci tensor
In an intro to GR book the Ricci tensor is given as:
$$R_{\mu\nu}=\partial_{\lambda}\Gamma_{\mu \nu}^{\lambda}-\Gamma_{\lambda \sigma}^{\lambda}\Gamma_{\mu \nu}^{\sigma}-[\partial_{\nu}\Gamma_{\mu \...
- 1,517
2
votes
0
answers
428
views
How do I extend the Lorentz transformation metric to dimensions>4?
How do I extend the general Lorentz transformation matrix (not just a boost along an axis, but in directions where the dx1/dt, dx2/dt, dx3/dt, components are all not zero. For eg. as on the Wikipedia ...
- 1,517
1
vote
2
answers
177
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What should I call an n>4 dimensional Minkowski metric?
I am manipulating an $nxn$ metric where $n$ is often $> 4$, depending on the model. The $00$ component is always tau*constant, as in the Minkowski metric, but the signs on all components might be +...
- 1,517
1
vote
2
answers
842
views
What kind of invariants are proper time and proper length?
Under the Lorentz transformations, quantities are classed as four-vectors, Lorentz scalars etc depending upon how their measurement in one coordinate system transforms as a measurement in another ...
- 3,284