# Questions tagged [tensor-calculus]

Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.

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### Is potential energy a scalar operator?

If a scalar operator $\hat{S}$ is defined as an operator that is invariant under rotations, i.e $$U^\dagger S U = S,\,\,\,\,\,\,\, U=e^{-i\theta\hat{\mathbf{J}}\cdot{\mathbf{n}}}$$ which is ...
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### Calculate Tensor and its transformations, transformation of derivatives of dependent variables

I had been learning tensor notation for a while and here's what's I have read: 1 Tensor had rank, denote two types covarient or contravariant. 2 $T(\__\alpha,\__\beta,\_\gamma)$ in place naming ...
### How can one prove $\int_V\text{d}V\ \vec A=0$, given that $\vec A\cdot \vec{\textbf{n}}=0$ and $\nabla\cdot\vec A=0$, without using tensor analysis?
In the course of learning electrodynamics, I was asked to solve the problem following: $\vec A$ is a vector which satisfies $\vec A\cdot \vec{\textbf{n}}=0$, where $\vec{\textbf{n}}$ is the normal ...