What is Indices: Definition and 205 Discussions

Hi, from Srednickis QFT textbook, we know the following coupling of Lorentz group representations: (2,1)\otimes (2,1) = (1,1)_A \oplus (3,1)_S, which yields \epsilon_{a b} as an invariant symbol. Generalising, we can look at (2,1)\otimes (2,1) \otimes (2,1) \otimes (2,1) = (1,1) \oplus...

Homework Statement "Evaluate: g^{\mu \nu} g_{\nu \rho} where ds^2 = g_{\mu \nu} dx^\mu dx^\nu , ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 " Homework Equations None necessary, just a notation issue The Attempt at a Solution Just using raising and lowering rules, I imagine each raising and...

Hi there, in Linearized theory we know that : gαβ = ηαβ + hαβ If I multiply out both terms by ηθαηλβ, wouldn't one get : gθλ = ηθλ + hθλ ? EQ1 But we already know gθλ = ηθλ - hθλ + O(h2) EQ2 How can we reconciliate EQ1 and EQ2 ? Was it an error to have raised the perturbation h with the η...

Homework Statement I have a tensor X^{μ\nu} and I want to make this into X_{μ\nu}. Can I do this by simply saying X_{μ\nu}=\eta_{μ\nu}\eta_{μ\nu} X^{μ\nu} ??

I have been doing a bit of studying for my optics course and I have often come across refractive indices or materials being presented as n-1 (which often makes a lot of sense). I was just wondering if there was a special term like for this format or if we still call it just the "refractive...

OK, I've looked around the net but there just doesn't seem to be a straightforward answer that doesn't require you to be an electromagnetics guru, so I'm hoping someone on here can help me out. I have a light wave incident to a planar interface, coming from a medium with complex refractive...

Homework Statement Given: Spherical blackbody with surface temperature of 30000K radius of 6.0 x 10^9 m located 123pc from earth Homework Equations Find the absolute and apparent bolometric magnitudes The Attempt at a Solution My camera needs batteries so I cannot post my work...

Hi have i got this corresct : g_{\mu\nu}g_{\mu\nu}T^{\mu\nu} = T g_{\mu\nu} = T_{\mu\nu} and is: g_{\mu\nu}g_{\mu\nu}u^{\mu} = g_{\mu\nu} u_{\nu} = u_{\mu}

Homework Statement As part of a problem I am doing I am asked to show uβ∂βuα = aα where u is 4 velocity and a refers to 4 acceleration. The way to do this is not immediately obvious to me, especially since the problem implies there should be a chain rule step involved which I am not seeing. I...

I was wondering if anyone could give me some info on what the miller indices of Inconel 600 and 690 alloys are. I know they are FCC structure, but does that automatically give them the conventional numbers, or is it something else since it is a complex alloy?

Hi All, I'm working on a little side-project (not school related) in Java for analyzing Financial Stocks (I understand the stuff I'm doing can be done online but I'm trying to learn some graphing/plotting in Java). Anyways, my question has to do with calculated EMAs (Exponential Moving...

Generally, Gamma matrices with one lower and one upper indices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally construct gamma matrices with two lower indices. There...

Homework Statement A marketing team is given a budget of 30,000 to advertise a new show. It wants to promote this show using two methods, internet and posters. The executives have decided that the overall budget used on the internet can't be greater than double the budget used on posters...

Homework Statement I'm not sure if this is the right section, but I also posted in the chemistry section. I'm taking a materials engineering class which involves a lot of chemistry. I attached the problem. Homework Equations The Attempt at a Solution Plane A: since the plane...

I was wondering how the indices of tensors work. I do not understand how the indices of tensors in can be used. For example, \eta _{\mu \nu }, the metric tensor, is like a matrix, and x^{u} is a contravector. How does this extend to notations such as T{_{a}}^{bc} and T{_{ab}}^{c}?

So, I have this equation: ^{137}_{55}Cs \rightarrow ^{137}_{56}Ba + e^- + \bar{\nu}_e What I don't like about it is that both 55 and 56 are left aligned and there is a gap between numbers and Ba symbol. I guess I could try to hand align them using spaces and negative spaces, but I also...

does anybody know the upper limit of the bcc and fcc metals like Fe, Cu, Ag? According to the fact that the planes with high (hkl) indices have small interplanar spacing d_hkl, the smallest spacing would be present. what is that? atomic diameter of a specifc metal?

Homework Statement A beam of light in air is incident on a stack of 4 flat transparent materials with indicies of refraction 1.20, 1.40, 1.32, and 1.28. If the angle of incidence for the beam on the first of the four materials is 60*, what angle does the beam make witht the normal when it...

So I am trying to use for loops to shift the index an array by a user inputted value. The code i have so far is printMessage(); cin >> choice; if(choice == 2){ cout << endl; cout <<"Please enter...

hi All, as the title suggests, I a not so clear on the difference between the two. in particular in solids, I have been looking at various approached to calculating the refractive index. But I´m not so clear on why there is two descriptions of we have a homogeneous medium. thnks!

Please read the following carefully. The point of the following is to distinguish between T^{\mu}_{\mbox{ } \nu} and T_{\mbox{ }\mu}^{\nu} which clearly involves a metric tensor. But when you want to go from component manipulation to matrix operations you have to be careful. Components are...

Hi! Given a matrix A of elements A_i\;^j, which is the right transpose: A_j\;^i or A^j\;_i ?

Homework Statement A simple cubic crystal with lattice parameter 0.5 nm has a plane which intersects atoms at the points (-0.5,-0.5,0), (1,-0.5,0.5) and (1,2.5,-1.5), where the coordinates have units of nm. What are the miller indices of the plane? Having read the relevant chapters of...

Homework Statement Consider the population model with dx/dt=rx(1-x)-ax/(1+x). Compute the normalized forward sensitivity indices of the (positive) internal equilibrium with respect to r and a. The default parameter values are r=4, a=3.Homework Equations SI(x,t)=(∂x/∂t)*(t/u)The Attempt at a...

I am struggling with my mathematics indices homework. I think I have some correct answers so far but I'm pretty stumpted on some others. How would I go about solving the following equations. Homework Statement 1) 25 to the \frac{1}{2} - \frac{5 to the -4}{5 to the -5} Homework...

Given that (√3)^7 + (√3)^5 + (√3)^3 + 42(√3) may be expressed as 3^κ, find the value of κ Now I know that (√3)^ 7 is the same as 3^3.5 so I have 3.5, 2.5 and 1.5 but i have no idea how to calculate 42 (√3). Please help :(

Homework Statement If : p2+q2+4r2 = pq+2qr+2rp Prove that : p=q=2r Homework Equations I am not sure but I tried using this equation : (a+b+c)2 = a2+b2+c2+2(ab+bc+ca) The Attempt at a Solution p2+q2+4r2 = pq+2qr+2rp p2+q2+4r2 -pq-2qr-2rp = 0 Now I can't factor. Its not...

(ABC)ij =Xk Xl AikBklClj where x is the sum of In the above equation which are the dummy indices and which are the free indices? I think i and j are free, and k and l are dummy. But I am not surre!

Homework Statement The task is to show the invariance of a given Lagrangian (http://www.fysast.uu.se/~leupold/qft-2011/tasks.pdf" ), but my problem is just in one step (which i got from Peskin & Schröder, page 70) which i can not reproduce due to my lack of knowledge regarding spinors. The...

i want to loop on K vector values K = [3 5 7 9 11] and have with me inside the loop the index of the current vector value if i made for K = [3 5 7 9 11] disp(K) end i'll not have the index of K values i mean when K=9 i want to know that I'm in index 4 how to make that??

hi, could someone explain the following statement, please? Why is the real data only shifted, but the Fourier space data is 'wrapped around'? The only difference should be: exp(k*x*2*i*Pi/N) in reals space vs. exp(-k*x*2*i*Pi/N) in Fourier space. Both have a periodicity of N. So why is there...

will the following actions be appropriate g^{\mu\sigma}\frac{dA_{\sigma}}{d\tau}=\frac{dA^{\mu}}{d\tau}Please let me know, I will be glad if you can explain too. thanks

A tank of water (nwater = 1.33) is co v e r e d w i t h a l a y e r o f oi l (noil = 1.48), a b o v e w h i c h is a i r ( n ~ r - - 1.00). W h a t a n g l e m u s t a b e a m o f l i g h t , o r i g i n a t i n g i n t h e t a n k , m a k e a...

If someone could please provide me with a simple explanation for observability indices I would be most grateful! According to wikipedia; "The Observability index (v) of a linear time-invariant discrete system is the smallest natural number for which is satisfied that rank(Ov) = rank(Ov + 1)"...

Hi, I always seem to have a problem with my indices... \Lambda^{\mu}_{\;\;\nu}\Lambda_{\bar{\nu}}^{\;\;\mu}= \frac{\partial x'^{\nu}}{\partial x^{\mu}} \frac{\partial x_{\bar{\nu}}'}{\partial x_{\mu}} Now, the first term I'm relatively sure is right (first lambad corresponds to first of the...

I would welcome advice on the practical issues of manipulating tensor indices, in particular how to determine the order of indices during calculations. Some of the following questions are probably simplistic but I have been unable so far to find a consistent answer. 1) Some texts use a unique...

Hi Guys, What are the milled indices of plane (see attached figure). Its very interesting...and I am receiving every-time different answer from others. Have a look. Shriphy

If: \delta x^\mu = a^\mu +w^{\mu}_{\nu}x^\nu How would we go about working out \delta_1 \delta_2 x^\mu This is apparently equal to: (w^{\mu}_{1}_\nu a^{\nu}_{2} + w^{\mu}_{1}_\lambda w^{\lambda}_{2}_\nu) x^\nu but I can't understand what is going on with the indices - can someone help me...

Sorry if this is a stupid question but I really want to understand this. If we have an operator that's defined in the following way: D_\mu \phi^a = \partial_\mu \phi^a - iA^{r}_{\mu}{(T_r)^a}_b\phi^b How would we go about working out: D_\mu D_\nu \phi^a What's confusing me is that the...

Hi, Say I have a 10x10 matrix, is there a simple code to finding the indices of the maximum value? I'm trying to use max() but there doesn't appear to be any option of actually returning the index, rather than the value. I don't need the value, just the position. Thanks, Mike

Bragg's law n.lambda=2d sin theta. d=1/{h^2/a^2+k^2/b^2+l^2/c^2} for orthorombic structure. thus d=n.lambda/2 sin theta=1/{h^2/a^2+k^2/b^2+l^2/c^2} lambda and theta are given. Look, there are two types/sets of unknowns in the d formula, they are miller indices h, k, l and lattice constant...

I'm trying to get my head around indexing x-ray diffraction patterns and this thought experiment stumps me. Let's say I have a crystal with a simple cubic lattice structure: http://ecee.colorado.edu/~bart/book/sc.gif I align a narrow x-ray beam incident on the crystal so that the x-ray...

If you look up the second quantization spin operator, you'll notice that there are two indices on the pauli vector for two possible spins. The operator sums over these two indices. Since the pauli vector is an unchanging quantity what do these indices physically correspond to?

Homework Statement Explain how we can determine Miller indices corresponding to the diffraction lines? Can someone explain it for me please? Homework Equations The Attempt at a Solution

Hi I am trying to figure out the physical interpretation of tensor indices. E.g., if we have an anisotropic material, then the tensor element of the susceptibility xx,y gives the response in the x-direction of an electric field in the y-direction. Lets not go up one dimension and look at...

"Pauli matrices with two spacetime indices" Hi all. This is my first post so forgive me if my latex doesn't show up correctly. I am familiar with defining a zeroth Pauli matrix as the 2x2 identity matrix to construct a four-vector of 2x2 matrices, $\sigma^\mu$. I'm trying to read a paper...

Hello. I was wondering if anyone here could help me understand this method I found described in the paper: "A Practical Approach for 3D Model Indexing by combining Local and Global Invariants" by Jean-Philippe Vandeborre, Vincent Couillet and Mohamed Daoudi for computing curvature indices...

Homework Statement I have an infinite series that looks like this: \sum_0^\infty n(n-1)d_nx^{n-1} + \sum_0^\infty n(n-1)d_nx^n + \sum_0^\infty d_nx^nI wish to combine all three sums so that they must all have same powers of x and start at same index. The second and third summations are fine...

Prime Indices & the Divisors of p'_n - 1 such that Divisors & Indices are equivalent for... p'_n an element of {N} | d'(n) < or = to 2 This set of integers is equivalent to 1 Union the Prime Numbers aka "Primes at the beginning of the 20th Century" where... d'_n denotes the number of divisors...

If j^\mu = ( j^0 , \vec{j} ), why does \partial_\mu j^\mu = \partial_0 j^0 + \vec{\nabla} \cdot \vec{j} surely when you take a dot product of four vectors you get a subtraction as in a^\mu b_\mu = a^0 b_0 - \vec{a} \cdot \vec{b} Maybe I'm forgetting something