# 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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### Covariance/contravariance and parallel transport

I am considering following problem. Let $\varphi$ be some scalar, $\eta^{\alpha \beta}$ be the Minkowski metric tensor and $g^{\alpha \beta}$ be the metric tensor of the curved spacetime. Let’s say ...
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### When can we take the action between two fixed times in a relativistic classical field theory?

Peskin and Schroeder give a brief outline of Lagrangian field theory on page fifteen in their Quantum Field Theory book, where they write: Lagrangian Field Theory The fundamental quantity of ...
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### How is tensor analysis useful to Relativity? [duplicate]

How does the knowledge of tensor analysis and Differential Geometry help us understand the equations of General and Special Relativity?
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### The Relationship between Coordinates and SpaceTime

I was reading a paper describing the contributions integral mathematicians and physicists have made in the advancement of physics by Michael Atiyah (https://www.jstor.org/stable/24111066), but have ...
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### If velocity $v^\mu$ is a contravariant tensor of rank 1 then shouldn't force be a mixed tensor of type (1,1)?

The covariant derivative of a (1,0) tensor is a mixed tensor (1,1) but this doesn't seem to be the case. Force is always regarded as a rank 1 tensor. The derivative of velocity is acceleration. I'm ...
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### If momentum is a covector, how does $p=mv$?

There are several explanations on this site    about why momentum is a covector while velocity is a vector. This distinction is important for the geometric description of classical mechanics. ...
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### How to tell if the covariant derivative of something is timelike or spacelike

How can I tell if the covariant derivative of something is timelike or spacelike?
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### Valid tensor expression?

The following given tensor expression is:$$A^i=B_i+C_i\tag{1}$$ which is invalid expression since the free index on L.H.S is in upper part and on R.H.S it is in lower part so to make valid tensor ...
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### Fokker-Planck equation for the Wigner function to covariance matrix

I cannot understand the derivation in Louis Garbe article (https://arxiv.org/abs/1910.00604) about how to obtain the covariance matrix equation from Fokker-Planck equation for the Wigner function in ...
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1 vote
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### Classical electromagnetism field strength with index up and down

In Classical electromagnetism, we know the Lagrangian density read $$\mathcal{L}=-\frac{1}{4}F_{\mu \nu}F^{\mu \nu}$$ where $$F_{\mu \nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$$ However, I ...
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### If the scattering amplitudes are Lorentz scalars, why is S-matrix Lorentz covariant?

All observers should agree on the probabilities: $\mathcal{P}(\mathcal{R}_1 \rightarrow \mathcal{R}_2)$ in an inertial frame $\mathcal{O}$ = $\mathcal{P}(\mathcal{R}_1' \rightarrow \mathcal{R}_2')$ ...
Considering the diffeomorphism covariance/invariance of General Relativity, is it possible to characterise mathematically the various kinds of possible transformations $x'^{\mu} = f^{\mu}(x)$? All of ...