Questions tagged [covariance]

How a quantity behaves under a change of basis vectors. This tag covers relativistic covariance, as well as contravariant and covariant tensors not necessarily in the context of relativity. DO NOT USE THIS TAG for statistical covariance.

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Covariant Formulation of E&M

Can anybody explain me what does mean the "covariant formulation of electrodynamics"? What does the covariant here mean? Invariance of Maxwell equations under Lorentz Transformations? In what way? ...
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Transformation law for Christoffel's first kind

I don't understand this particular part in this image. I am following schaum's series book on "vector analysis". I didn't find any explanation for it. I also tried searching in Internet and somewhere ...
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Literature advice: Covariant formulation of classical physics [duplicate]

I am looking for a literature advice about the following. I'ld like to review classical physics (basically all undergrad / grad stuff) under the aspects of a modern covariant formulation with exterior ...
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Usefulness of Curl and Divergence as Multilinear Maps

Early in differential geometry, texts typically reformalize our usual gradient, divergence and curl operators as covariant tensors rather than vectors. This is primarily motivated by the observation ...
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Since all frames of reference are equal, can we treat the Earth as fixed?

Since Einsteins GR tells us all the frames of reference are equal, is there anything invalid about treating the Earth as unmoving and the universe itself rotating? Other than the fact that the ...
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Does the covariant derivative still give divergence in skew coordinates?

I stumbled upon the formula $\,\,div \, \vec{F}=F^{\mu}_{\,\,\,;\mu}$. Does this still hold true in skew coordinates? I can picture it working geometrically in orthogonal coordinates, but in skew ...
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Lagrangian transformation [closed]

I want to prove that the Lagrangian transformation is covariant for $x_{i}\rightarrow q_{i}(x)$ and $x_{i}\rightarrow q_{i}(x,t)$. So far I've proven that it holds for the first transformation as ...
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Why are Maxwell's equations not Galilean invariant? [closed]

So i am writing an essay on the conflict between galilean invarience and maxwell's electromagnetism. I am struggling to come up with 3 evidences that they conflict because I have a mediocre ...
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Why do we raise and lower indices of tensors of various groups with the invariants of that group?

If $T_{ij}$ is tensor that transforms under $SO(N)$ then apparently (according to what I have been told) it does not matter whether we put the indices up or down. If we instead have a tensor that ...
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A postulate in the beginning of special relativity

There’s a postulate in special relativity as following: Physics laws are identical in all inertial reference frames. I’m a math student, recently when I reviewed special relativity before learning ...
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Symmetry under Lorentz transformation: precise definition

I am studying QFT but I need to fill some gaps in my comprehension of special relativity (I didn't study it very well and I know I still misunderstand things in S.R). In my book it is written: " A ...
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Tensor in different coordinate system

I have the tensors $F_{\mu\nu}$, $F^{\mu\nu}$ in coordinate system $(t,x,y,z)$ and want to transform these to coordinate system $(t',x',y',z')$ just by multiplicating matrices. My idea was to ...
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State amplitude and field operator covariance in QFT

I'm studying QFT on Bogoliubov-Shirkov's "Introduction to the theory of quantized fields" (3d edition). In $§9.3$ they discuss transformation properties of quantum states and operators in QFT. Given ...
I know that tensors are object we use in general relativity to describe phenomenon. They have the property to have the same expression in various coordinates systems. For example if I take : $\... 0answers 63 views Commutator relation of EM Field Covariant? I read that for quantization of the EM-Field, you demand the canonical equal-time commutation relations: $$[A^\mu(\vec{x},t), \pi^\nu(\vec{y},t)] = i \hbar g^{\mu \nu} \delta^3(\vec{x} - \vec{y}).$$ ... 3answers 482 views Why is the inner product not invariant under general coordinate transformations? This came up in some of my reading (Introduction to Tensor Calculus by Kees Dullemond & Kasper Peeters, page 15). Why is the inner product not invariant under general coordinate transformations? ... 3answers 469 views Why is there an emphasis on tensor equations in GR? In my understanding the purpose of using tensor equations in GR is to ensure that they are true in all coordinate systems. I understand that writing equations tensorially ensures this will be the case;... 2answers 337 views Raising and lowering covariant and contravariant bases The vector$\textbf{a} = a_{i}\textbf{e}^{i}$in terms of covariant components. In terms of contravariant components,$\textbf{a} = a^{i}\textbf{e}_{i} = a^{j}\textbf{e}_j$. Thus,$a_{i}\textbf{e}^{i} ...
Consider a classical vector field $V^\mu$ on a curved background. We make a 3+1 split of coordinates into $t,x^i$, where $x^i$ are coordinates on spatial hypersurfaces $\Sigma$ and $t$ the parameter ...