Covariant Definition and 361 Threads

How can you tell if an equation is covariant just by looking at it. Please try and keep explaniation to text more than equations.

I'm starting to learn differential geometetry on my own, but I'm having a little trouble figuring out the difference between covariant and contravariant vector fields. It seems that contravariant fields are just the normal vector fields they introduced in multivariable calculus, but if so, I...

title says it all. I've heard these two phrases. Lorentz invariant: Equation (Lagrangian, or ...?) takes same form under lorentz transforms. Lorentz covariant: Equation is in covariant form. I'm don't think I know what I mean when I say the latter. Can someone elucidate the...

What is meant by " if an electron has size it would be difficult to be make covariant" in quantum field theory.Does this mean the electron would behave differently in different frames of reference,or does it just mean that the electron would not be in a state that allows it to fit into the...

I am doing the excercises on Chapter 2 of Ziebach's new book A First Course in String Theory. Part (b) of Problem 2.3 asks us to show that the objects \partial/{\partial x^{\mu}} transform under a boost along the x^1 axis in the same way as the a_{\mu} do. In other words, to show the...

Hi Given the Riemann-Christoffel Tensor : R_{i{\text{ }},{\text{ }}jk}^l = \partial _j \Gamma _{ik}^l - \partial _k \Gamma _{ij}^l + \Gamma _{ik}^r \Gamma _{jr}^l - \Gamma _{ij}^r \Gamma _{kr}^l I'm looking for the proof : \nabla _t R_{i,rs}^l = \partial _{rt} \Gamma _{si}^l -...

It's possible to do the tensor product of two contravariant vectors? It's possible to do the tensor product of two covariant vectors?

A spin foam is a "mousse de spin" On Friday Rovelli is giving a symposium talk on spin foams and he was Etera Livine's thesis director. My uninformed guess is that Rovelli will talk about Livine's thesis and in particular chapter 8 (Covariant loop gravity) which reflects potentially important...

In the online text on differential geometry http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/pdfs/DiffGeom.pdf The author calls the "derivative along the curve" (aka absolute derivative) the "covariant derivative" which is wrong. It's on box 8.2 on page 59. Does anyone...

Any books recommended for dummies? All books that I've found starts with contraviant and covariant tensor, which seems misleading to me.

I have a little question. I hope someone can help me. When we learn the theory of relativity and its formalism, we'll meet concepts : covariant and contravariant, such as covariant vector, covariant tensor... I wonder that why we need to use the concepts ? What are advantages of them ? I...