Covariant Definition and 345 Threads

Can you give me the definition of exterior covariant derivative or any reference web page ? Wiki does not involve enough info.I am not able to do calculation with respect to given definition there. Thanks in advance

Here are some papers on the covariant entropy bound conjectured by Raphael Bousso http://arxiv.org/abs/hep-th/9905177 http://arxiv.org/abs/hep-th/9908070 http://arxiv.org/abs/hep-th/0305149 It would be a significant development if the conjectured bound could be proven to hold in LQC...

Hi. I am attempting to gain some intuition for what the covariant derivative of a tensor field is. I have a good intuition about the covariant derivative of vector fields (measuring how the vector changes as you move in a particular direction), and I understand how to extend the covariant...

When we derive equation of motion by variation of the action, we use rules of ordinary differentiation and integration. So only ordinary derivatives can appear in the equation. Now in general relativity we are supposed to replace all those ordinary derivatives by covariant derivatives. Is that...

Sorry, but some of you may think this is a stupid question. (I'm only 16 years old.) I have just now gotten into the field of tensors and topology, after studying vector calculus and differential equations and I have two questions: a) What exactly is a covector? b) What is the...

Hi, I'm trying to verify that the covariant derivative of the metric tensor is D(g) = 0. But I have a few questions: 1) This is a scalar 0 or a tensorial 0? Because it is suposed that the covariant derivative of a (m,n) tensor is a (m,n+1) tensor, and g is a (0,2) tensor so I think this 0...

Homework Statement Help! I wish to prove the following important statements: (1) The presence of Christoffel symbols in the covariant derivative of a tensor assures that this covariant derivative can transform like a tensor. (2) The reason for this is because, under transformation, the...

Homework Statement Show that \frac{\partial\phi}{\partial x^{\mu}} is a covariant four vector . Homework Equations All covariant four vector transformations . The Attempt at a Solution I really didn't understand what question implies . How can this vector be showed as being a...

Homework Statement I am trying to show that the components of the covariant derivative [tex] \del_b v^a are the mixed components of a rank-2 tensor. If I scan in my calculations, will someone have a look at them? Homework Equations The Attempt at a Solution

Hi. I'm considering the covariant derivative \nabla_\mu V^\nu = \partial_\mu V^\nu + \Gamma_{\mu\nu}^\lambda V^\lambda in spherical coordinates in flat 3D space (x = r cos sin, y = r sin sin, z = r cos; usual stuff). Now I wrote down the gradient of a scalar function f, for which I got...

Homework Statement Can someone explain/help me prove the formulas \vec{e_a}' = \frac{ \partial{x^b}}{\partial x'^a} \vec{e_b} \vec{e^a}' = \frac{ \partial{x'^a}}{\partial x^b} \vec{e^b} I do not understand why the partial derivative flip? Homework Equations The Attempt at a Solution

just a quick query, I know that, \nabla_0 A_{\alpha}= \partial_0 A_{\alpha} - \Gamma^{\beta}_{0 \alpha} A_{\beta} But what does \nabla^0 A_{\alpha} equal?

I am not as well read as most of the people in here so I thought I would ask you guys first. What work has been done in the way of developing a covariant field theory? I'm going to ramble for just a little bit so try to follow. It seems to me that QFT is built on two principles Poincare...

In anglo-american literature -a physical quantity is invariant if it has the same magnitude in all inertial reference frame, -an expression relating more physical quantities is covariant if it has the same algebraic structure in all inertial reference frames (rr-cctt) ? Thanks in advance

I'm not really sure where to put this, so I thought it post it here! I'm reading through my GR lecture notes, and have come across a comment that has confused me. I quote Now, I don't really see how this is true. For example, consider a scalar field f. The covariant derivative of this is...

I've heard of something called a covariant derivative. what motivates it and what is it?

Loosely speaking or Intuitively how should one understand the difference between Lie Derivative and Covariant derivative? Definitions for both sounds awfully similar...

Is there any relationship between the Lie (\pounds) and covariant derivative (\nabla)? Say I have 2 vector fields V, W and a metric g, the Lie and covariant derivative of W along V are: \pounds_{V}W = [V,W] V^\alpha \nabla_\alpha W^\mu = V^\alpha \partial_\alpha W^\mu + V^\alpha...

Dear Fellows, Do anyone have an idea of whether there must be a system tensor in order to be able to transform from the covariant form of a certain tensor to its contravariant one? This is a bit important to get rigid basics about tensors. Schwartz Vandslire...

Does anyone know the physical (or historical) basis for the terms covariant and contravariant? I'm guessing a particular class of mapping always tranforms components (of ..?) in exactly two different ways, so I'm wondering what the mappings are (Change of coordinate charts? Lorentz...

It's physics based but actually a maths question so I'm asking it here rather than the physics forums. I = \int \mathcal{L}\; d^{4}x I is invariant under some transformation \delta_{\epsilon} if \delta_{\epsilon}\mathcal{L} = \partial_{\mu}X^{\mu} for some function/tensor/field thingy X^{\mu}...

I find the covariant version of loop quantum gravity http://arxiv.org/abs/gr-qc?papernum=0608135 more appealing than the usual LQG approach. What the experts think?

That's a crucial point of GR ! And I have always problems with that. Back to the basics, with your help. Thanks Michel

Why we have to definte covariant derivative?

I read some books and see that the definition of covariant tensor and contravariant tensor. Covariant tensor(rank 2) A'_ab=(&x_u/&x'_a)(&x_v/&x'_b)A_uv Where A_uv=(&x_u/&x_p)(&x_u/&x_p) Where p is a scalar Contravariant tensor(rank 2) A'^uv=(&x'^u/&x^a)(&x'^v/&x^b)A^ab Where A^ab=dx_a...

If we define the Gradient of a function: \uparrow u= Gra(f) wich is a vector then what would be the covariant derivative: \nabla _{u}u where the vector u has been defined above...i know the covariant derivative is a vector but i don,t know well how to calculate it...thank you.

The covariant derivative is A^\mu_{\sigma} = \frac{\partial A^\mu}{\partial x_{\sigma}} + \Gamma^\mu_{\sigma \alpha}A^\alpha ... why?

How is the covariant derivative derived?

Can anyone explain to me what is contravariant and covariant? I just know that they are tensors with specific transformation properties (from website of MathWorld), i also know that the relation between two is the -ve sign. Then dose it mean that: given a 4-velocity of a particle is the...

I am trying to solve an exercise from MTW Gravitation and the following issue has come up: Let D denote uppercase delta (covariant derivative operator) [ _ , _ ] denotes the commutator f is a scalar field, and A and B are vector fields Question: Is it true that [D_A,D_B]f = D_[A,B]f ?

We all know that time-ordering depends on the choice of Lorentz frame. So my question is somewhat obvious... Please give me a hint on where to look up that problem, eg. why the S-matrix theory is covariant. I guess the time-ordering prescription is implicitly defined for each single...

Hello! I am trying t solution Navier-Stokes equation and I cannot find something about Laplacian. I would like to solution Laplace’a equation for each component.I am trying to transform cylindrical coordinate. I would like to search equation for covariant derivative. For divergence of a...

I've already handed in my (I can only assume) incorrect solution, but I just felt like posting, though I'm not sure if anyone will be able to help. I have a rank-2 covariant tensor, T sub i,j. This can be written in the form of t sub i,j + alpha*metric tensor*T super k, sub k (I hope my...

Since there are some equations in my question. I write my question in the following attachment. It is about the covariant derivative of a contravariant vector. Thank you so much!

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...