# 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.

622 questions
Filter by
Sorted by
Tagged with
1 vote
94 views

### Challenging Cauchy's Stress Tensor: Objectivity and Generalization of Divergence Theorem

I'm investigating the limitations of the Cauchy stress tensor model in classical continuum mechanics, specifically focusing on its compliance with the principle of material frame indifference (MFI) ...
• 373
1 vote
43 views

### A covariant derivative computation in General Relativity [duplicate]

I am trying to compute $\nabla^\mu\nabla^\nu R_{\mu\nu}$. I proceed as follows: \begin{align} \nabla^\mu\nabla^\nu R_{\mu\nu}&=g^{\mu\rho}g^{\nu\lambda}\nabla_\rho\nabla_\lambda R_{\mu\nu} \\ &...
• 350
137 views

### How does the bulk-to-boundary propagator transform under diffeomorphisms?

In AdS/CFT, the bulk-to-bulk propagator can be obtained as the limit of the bulk-to-bulk propagator with one point approaching the boundary. For example in the scalar case K_{\Delta}(...
60 views

### 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, ...
• 1,714
173 views

• 11
1 vote
25 views

• 1,290
1 vote
84 views

### 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 ...
95 views

### 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. ...
192 views

### 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 ...
• 530
1 vote
22 views

### Tramsformation of spatial components of the 4-force

I'm trying to learn special relativity by myself. I've been reading the Griffith's chapter about relativistic dynamics and electrodynamics (chapter 12), but one thing it's not clear to me. I've been ...
• 530
125 views

### Are the stress and strain tensor covariant or contravariant?

My question is related to this question but I don't find the answer there to be completely satisfactory. The displacement of an elastic medium is a contravariant quantity, which I think is pretty ...
68 views

### 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
1 vote
91 views

• 401
22 views

513 views

### Inverse of the covariant derivative

Given the covariant derivative of some tensor, for the sake of this example a covariant vector: $$\nabla_\mu A_\nu$$ Is there a well-defined inverse operation on the covariant derivative such that it ...
• 633