Index notation Definition and 114 Threads

I've already posted a couple of index notation questions on here and I've gotten very helpful responses. So I thought I'd try my lucky again, though I'm a little more stumped on this question than I was on the others... Let \vec{x} be the position vector and \vec{r} the radial unit vector. In...

How do I make sense of the index notation expression r_j r_i p_j ? What I really *want* it to be is \vec{r} (\vec{r} \cdot \vec{p}) And it turns into this, as long as I can commute the r_i[/tex] and r_j...right? (By the way, here \vec{r} is just the position vector and...

I'm trying to simplify the expression (\hat{r} \times \vec{\nabla}) \times \hat{r}, where \hat{r} is the radial unit vector, using index notation. I think I'm right to write this as: ((\hat{r} \times \vec{\nabla}) \times \hat{r})_i =...

Homework Statement hey just wondering if anyone could show the the working for the index notation in the attachment it would be greatfully appreciated. thanks. the answer is there I am just looking for the working. Homework Equations The Attempt at a Solution

I'm differentiating with respect to Grassman variables, and I'm getting something very inconsistent: Suppose \xi and \chi are two-component, left-handed, grassman-valued spinors. Now, I take derivatives with of the product, \xi^a \chi_a, respect to \xi two different ways, and denote their...

Homework Statement Prove vector identity \nabla x\nabla\phi = 0 using index notation. Homework Equations \nabla x A = E[SIZE="1"]jrt\partial[SIZE="1"]rA[SIZE="1"]t The Attempt at a Solution I'm treating this as \nablax A, where A = del \Phi = E[SIZE="1"]tpq\partial[SIZE="1"]p\Phiq...

How does abstract index notation work? What do the the indices represent? I know the Lorentz transformation tensor in arbitrary direction, so if you want to use a specific tensor in an example, that would be a good one.

Hi, does anyone know a link showing how to calculate curl with a Levi-Civita tensor. I can't figure it out but I am sure if I could see an actual example would be able to work out what is going on. Thanks.

Homework Statement Find the dual vector of the following tensor: 6 3 1 4 0 5 1 3 2 Homework Equations dj= EijkTik Where Eijk = 1 if ijk=123, 231, 312 Eijk = 0 if i=j i=k or j=k Eijk = -1 if ijk = 132, 213, 321 The Attempt at a Solution Ok...

This is a brief tutorial to cover the basics of index notation which are useful when handling complicated expressions involving cross and dot products. I will skip over a lot of technicalities (such as covariant and contravariant vectors) and focus on 3 dimensions - but all of what I say here...

A professor of mine recently remarked that dirac notation is easily the best in physics & we'd quickly realize this once we take a course in relativity. I've already taken the course & I find myself disagreeing with him, but maybe that's only because I enjoy relativity more. Curious what you...

I am playing around with learning index notation for tensors, and I came across the following where C is a 0th order tensor: E_{ijk} \partial_j \partial_k C = 0 I believe this equates to \nabla \times \nabla C. I don't understand why this comes out to 0. Any ideas? Also, I am trying...

I've been stuck with this problem since a while.. thought I'd ask here; \nabla \times \dfrac{\vec{A} \times \vec{r}}{2} solving normally isn't any problem, but I have to do it with index notation, where A is an arbitrary vector field and r is the position vector) This is how far I can...

hello, i just started learning index notation in my engineering class, and I am having some trouble. one of the problems on my homework was: putting this in index notation: \vec{f}=g \frac{m_1m_2}{\vec{r}^2} \ \frac{\vec{r}}{\sqrt{\vec{r}^2}} and then another problem that reads...