All Questions
Tagged with tensor-calculus covariance
269
questions
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144
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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
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1
answer
71
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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
2
votes
1
answer
186
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How does the covariant vector transformation rule come?
As far as I understand, if a contravariant vector transforms in the form:
$$\vec{x}'=A\vec{x}.$$ (Where $A$ is the transformation matrix)
Then the covariant vectors shall transform as
$$\tilde{w}'=(A^{...
- 33
3
votes
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68
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Counting independent components of Lorentz tensor
Say I have Lorentz tensors $A^{\mu\nu}$ and say this Lorentz tensor is symmetric under $\mu \Leftrightarrow \nu$ and there are only $p^\mu$ and $q^\mu$ as the physical Lorentz vectors involved. If so, ...
- 857
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165
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How do we know the tensorial form of the Maxwell equations manifestly transform as tensors?
In Sean Carroll's book he derives the two tensorial Maxwell equations from the four non-tensorial equations. I noticed that one of these equations is the Bianchi identity for the electromagnetic ...
- 103
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79
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Implicit assumption behind the definition of scalar, vector, and tensor fields
Let me consider a field
\begin{align}
A^\mu(x) \equiv dx^\mu,
\end{align}
which seems to be a vector field trivially.
However, to check that, we calculate as
\begin{align}
A'^\mu(x') \equiv dx'^\mu = \...
- 353
1
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85
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Del operator confusion [closed]
The very first thing my textbook says is that the Del operator is defined as:
$$\vec{\nabla}=\vec{a}^i\nabla_i$$
Where $\nabla_i$ is the covariant derivative and " $\vec{a}^i$ is the curvilinear ...
- 267
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99
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What is the intuition or the derivation of covariant derivative?
I asked this question in mathematics but the answer I got was a bit too abstract for me so I hope that my fellow physicists can give me more of an intuition or an easier explaination of my question. ...
- 267
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209
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Formulation of the Bianchi identity in EM
I'm trying to understand, as a self learner, the covariant formulation of Electromagnetism. In particular I've been stuck for a while on the Bianchi identity. As I've come to understand, when we ...
- 540
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79
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How to derive the form of transformation operators in Einstein notation?
I've been reading through MWT to try and drill home some of the fundamentals a little more. I've gotten to their derivation of the form of Lorentz Transformation in Einstein notation and how they act ...
- 269
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92
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Is the Lie derivative in a coordinate direction covariant?
Considering a partial derivative of a vector field $w^a$ in x-direction (also called here 1-direction) I can write it as $$\frac{ \partial w^a}{\partial x^1 } = \partial_1 w^a - \Gamma^a_{1c} w^c + \...
- 9,778
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70
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Contravariant or covariant tensor in electromagnetism?
I have a question about the following 2 tensors: the permittivity tensor and Maxwell's stress tensor. I was wondering if someone can explain which one is contravariant or covariant, and show why that ...
- 101
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389
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What is the difference between covariant and contravariant tensors? [duplicate]
What is the difference between covariant and contravariant tensors?
I have been seeing in a lot of problems but I´m not sure what is the difference or if is only a equivalent notation.
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99
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Divergence and Covariant/Contravariant Transformations
I am trying to understand the covariant/contravariant representation of the divergence in different coordinate systems.
Normally, we would get in the holonomic basis the following divergence according ...
- 47
1
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1
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157
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Invariants from the covariant derivatives of a scalar field
I am reading Theoretical minimum: Special Relativity and Classical Field Theory where you construct a Lagrangian for the field by the argument that it would be invariant under the Lorentz ...
- 357