# 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.

364 questions
Filter by
Sorted by
Tagged with
314 views

### Providing an intuitive description of scalar and vector quantities in physics [closed]

Often the standard introduction to the concept of scalars and vectors in physics is something along the lines of: A scalar is a quantity that is completely described by a single number (it has no ...
6k views

### What is the Difference between Lorentz Invariant and Lorentz Covariant? [duplicate]

Like my title, I sometimes see that my books says something is Lorentz invariant or Lorentz covariant. What's the difference between these two transformation properties? Or are they just the same ...
348 views

833 views

### What is “a general covariant formulation of newtonian mechanics”?

I am a little confused: I read that there are general covariant formulations of Newtonian mechanics (e.g. here). I always thought: 1) A theory is covariant with respect to a group of transformations ...
1k views

### Einstein Summation Convention: One as Upper, One as Lower?

My question refers to the often specified rule defining Einstein Summation Notation in that summation is implied when an index is repeated twice in a single term, once as upper index and once as lower ...
171 views

### Four Vectors in SR and QFT

I'm covering both special relativity and quantum field theory in the summer. I'm currently using Spacetime Physics by Taylor and Wheeler to cover SR. Since I'm covering SR on the side with QFT, I'm ...
1k views

### Is Young's Modulus a Lorentz Scalar?

If a spring is at rest and lies along $X$ axis in a frame $O$ with a spring constant $k_{0}$ then its spring constant in a frame $O'$ which is moving with a speed $v$ at an angle $\theta$ with the $X$ ...
178 views

828 views

### Using $\sqrt{-g}$ in integrals of proper volume

I am a little confused over integration using proper volume element. When do we use $\sqrt{-g}$ in calculations? For example, in many calculations involving stars, say when using TOV equation, this ...
456 views

351 views

449 views

### contravariant and covariant vectors and their orthogonality in Euclidean space

I am reading this paper Sigma Coordinate - Contravariance and covariance and I understand how covariant and contravariant vectors are defined mathematically Covariance and Contravariance and I had ...
674 views

### What does coordinate invariance mean?

I would like to really understand what the mathematical as well as Physical meaning of coordinate invariance is. I have pretended to know what this means, but upon thinking a little harder today, I am ...
274 views

### Is there any way to justify or derive the form of the Lorentz force from relativity theory?

Lorentz force is in this form: $$\vec{F}=q[\vec{E}+\vec{u}\times\vec{B}]$$ As we know, it is Lorentz-invariant. Is there any way to justify or derive its form from relativity theory?
234 views

### Canonical second quantization vs canonical quantization with multisymplectic form in AQFT

First of all, I'm a mathematician that knows less than the basics of QFT, so forgive me if this question is trivial. Please, keep in my mind that my background in physics is very poor. 1) The usual ...
142 views

51 views

### Is there a general procedure for covariantizing equations?

I am currently attempting to derive covariant forms of equations whose domains are D=3 space. I am considering Lorentzian $(\mathbb{R}^4, \Omega, x, \nabla)$, where $\Omega \subset\mathbb{R}^4$ has a ...
92 views

### solutions of wave equation with cubic term

Does the following equation $$\nabla^\mu \nabla_\mu \psi + a \psi^3 = b \psi$$ where $\psi$ is a real function, $a$ and $b$ are real constants, have other solutions that extend beyond a one ...
4k views

### Gradient, divergence and curl with covariant derivatives

I am trying to do exercise 3.2 of Sean Carroll's Spacetime and geometry. I have to calculate the formulas for the gradient, the divergence and the curl of a vector field using covariant derivatives. ...