# Questions tagged [differentiation]

Differentiation is the set of techniques and results from Differential Calculus, concerning the calculation of derivatives of functions or distributions.

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### Curl operator in Schwarzschild metric

I'm trying to write down the curl operator explicitly for a Schwarzschild metric in cylindrical coordinates. I am trying to use the general expression of the curl operator in orthogonal curvilinear ...
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### How is Infinitesimal coordinate transformation related to Lie derivatives?

I am reading the book "Gravitaion and Cosmology" by S. Weinberg. In section 10.9, while discussing Lie derivatives of tensors of different ranks, he makes a general comment: The effect of an ...
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### Commutativity Variation and derivative

When in general is true that $\nabla_{\mu}\delta=\delta\nabla_{\mu}$ where $\nabla_{\mu}$ is covariant derivative? I was thinking this when one has to find the equations of motion for example in ...
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### Dependence of scattering amplitudes on Mandelstam variables

It is well-known that scattering amplitudes in QFT are tensors, hence e.g. scalar amplitudes /written in momentum space/ depend only on the Mandelstam variables of the external momenta, involved in ...
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### Is my thinking correct for partial derivatives and tensors?

So I was transforming the affine connection and I ended up with a term like this: $$\frac{\partial^2 x'^a}{\partial x'^b \partial x^p}$$ where $x$ and $x'$ are two different coordinate systems ...
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### Covariant derivative with respect to commutator

I have some confusion with the notion of $\nabla_{[A, B]}\bf{v}$, that expression, with a commutator of vector fields as the subindex of the connection appears for instance in the definition of the ...
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### “Chain Rule” for functional derivatives in the context of a derivation of the geodesic equation by the stationary proper-time principle

I have been working on deriving the geodesic action via finding the stationary points of the proper-time integral for a massive point particle. Consider a space-time manifold $M$ ($\dim M=4)$ equipped ...
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### What does lowercase-delta mean in Noether's first theorem?

Most expressions of Noether's Theorem I have come across do not use lowercase delta, but a couple sites do. I am confused....... Check out page 21 of the June 23 issue of 'Science News' ...
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### Question about Covariant Derivatives in General Relativity

I'm following the differential approach of Schutz' book where vectores are geometrical objects written as \begin{equation} \vec{V}=V^a\ \vec{E}_a \end{equation} Where $V^a$ are the components of the ...
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### Why does the material derivative and transport theorem look different?

Reynolds transport theorem says that $\frac{d\int\phi}{dt}=\int\left(\frac{\partial\phi}{\partial t} + \nabla\cdot(\phi\otimes v) \right)$ Why is the material derivative not defined as what's ...
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### Vector Derivative: General Case

From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector". In this section, towards the end, ...
This is essentially a follow up to my question here since I seem to have some difficulties regarding the differences between partial and total derivatives. Consider a Lagrangian density \mathcal{...
I was looking at a derivation of the Barometric formula which reads like this: Consider a flat disc of air of mass $\mathrm{d}m$ at distance $h$ above the ground of mass $\mathrm{d}m$ and thickness ...