# What is Indices: Definition and 205 Discussions

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1. ### I How do you differentiate between the inner and lower indices on a Lambda tensor?

$${\Lambda}^{i}_{j}$$ When indices are written on top of one another I am confused wich is the inner index and which is the lower one when we lower the upper index.

8. ### Prove the given equation that involves indices

My approach; $$(a-a^{-1})(a^{\frac {4}{3}} + a^{\frac {-2}{3}}) =(a-\frac {1}{a})(a^{\frac {4}{3}} +\frac {1}{a^{\frac {2}{3}}}) =(\frac{a^2-1}{a})(\frac{a^2+1}{a^{\frac {2}{3}}}) =\frac{a^4+a^2-a^2-1}{a^{\frac {5}{3}}} =\frac{a^4-1}{a^{\frac {5}{3}}}$$ now at this point i multiplied both...
9. ### I Raising & Lowering Indices: Q&A on Relativity

I am reading《Relativity - An Introduction to Special and General Relativity》 my question: ##1=-\eta_{44}L^{n{'}}{_4}L_{n{'}}{^4}=-\eta^{n'}{^{m'}}L_{n{'}}{_4}L_{m'}{_4}## ##\eta## is Minkowski Metric，##L## is Lorentz transformation matrix... 1.Since ##-\eta_{44}##=1,what's the usage of it...
10. ### A Special Relativity: A^μ_ν Differences Explained

Can someone explain me difference between A^{\mu}_{\hspace{0.2cm} \nu} A^{\hspace{0.2cm} \mu}_{\nu} and A^{\mu}_{\nu}?
11. ### I Raising/Lowering Indices w/ Metric Tensor

I'm still confused about the notation used for operations involving tensors. Consider the following simple example: $$\eta^{\mu \sigma} A_{\mu \nu} = A_{\mu \nu} \eta^{\mu \sigma}$$ Using the rules for raising an index through the (inverse) metric tensor ##\eta^{\mu \sigma}## we get...
12. ### Solve for ##m## in this equation that involves indices

Find value of ##m##, given ##\frac {8^m + 27^m}{12^m + 18^m}##= ##\frac {7}{6}##
13. ### I Linearized Gravity & Metric Perturbation when Indices Raised

I have just met linearized gravity where we decompose the metric into a flat Minkowski plus a small perturbation$$g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu},\ \ \left|h_{\mu\nu}\ll1\right|$$from which we 'immediately' obtain $$g^{\mu\nu}=\eta^{\mu\nu}-h^{\mu\nu}$$I don't obtain that. In my rule book...
14. ### DP: What's a subproblem space? Why have varying indices for a subproblem?

In dynamic programming: 1. what is the definition of the space of subproblems? does it have a mathematical definition? 2. why is it necessary to have an arbitrary index for the subproblem to vary? To elaborate on question 2, I've taken the following paragraph from chapter 15.3 in...

39. ### How Do You Calculate Hexagonal Miller Indices Correctly?

Homework Statement Homework Equations find intercept ==> reciprocal ==> reduction ==> (hkl) miller indices ==> i ==> (hkil) miller indices The Attempt at a Solution by using axis a1 a2 z, intercept: a = 0, b = inf, c=inf reciprocal: a= inf,b=0,c=0 (hkl)=(inf 0 0) i=-(h+k) = no conclusion I...
40. ### A Calculating Indices: Solve the Mystery

Would anyone explain how the calculation in the picture was carried out? (the second equal sign) I don't seem to be able to get the indices right.
41. ### EoM from action, indices confused, (QFT)

Homework Statement Using the E-L equations to get the EoM from the action. Homework Equations I am using E-L equations in the form: ## \frac{\partial}{\partial_u} \frac{\partial L}{\partial_u \phi}-\frac{\partial L}{\partial \phi} ## where ##L ## is the Lagrangian The Attempt at a...
42. ### Contracting dummy indices tensors

Homework Statement We've been told there's this operation called 'contraction' where if you have a superscript and a subscript that are the same they cancel. I don't understand how that works, partly in the sense that we haven't got round to what the superscripts and subscripts actually mean...
43. ### Contracting dummy indices tensors

Homework Statement Write out this covariant derivative in terms of partial derivatives and Christoffel symbols: ##\nabla_{\mu} S^{\nu}_{\nu \rho}## Homework EquationsThe Attempt at a Solution I think you can contract that so it reads ##\nabla_{\mu} S_{\rho}##, in which case the solution...
44. R

### A Wick contraction for same indices (Zee, "QFT in a Nutshell")

Hey, I thought I understood Wick contractions but a formula in Zee's "Quantum Field Theory in a Nutshell" disproved me: In the section on Feynman Diagrams it is tried to evaluate the "four-point Green's function" in (I.7.10) by the integral  \int_{-\infty}^\infty \left ( \prod_m \mathrm{d}...
45. ### I Miller indices for hexagonal crystal systems

Hi everyone, to find the draw the direction for a given miller index say, [1234] we first convert this miller index consisting of 4 indices into one containing 3 indices. To do so, we have a set of formulae prescribed in almost every book. Sadly I haven't been able to come across a single book...
46. ### Can text files display sub or sup indices?

Is there any way to show sub or sup indices in a text file such as this Ab? Text files are very easy to use. They are fast, can be opened fast and created easily. Thank you.
47. ### I Metric tensor : raising/lowering indices

Hi everyone, I'm currently studying Griffith's Intro to Elementary Particles and in chapter 7 about QED, there's one part of an operation on tensors I don't follow in applying Feynman's rules to electron-muon scattering : ## \gamma^\mu g_{\mu\nu} \gamma^\nu = \gamma^\mu \gamma_\mu## My...
48. ### Indices of refraction when wavelengths are given

Homework Statement A parallel beam of light containing two wavelengths, λ1= 400 nm and λ2= 650 nm, enters the silicate flint glass (at a angle of 41 degrees, relative to normal) of an equilateral triangle (60 degrees at each angle) prism. At what angle, relative to the normal, does each beam...
49. ### I Lorentz group, boost and indices

Compare this with the definition of the inverse transformation Λ-1: Λ-1Λ = I or (Λ−1)ανΛνβ = δαβ,...(1.33) where I is the 4×4 indentity matrix. The indexes of Λ−1 are superscript for the first and subscript for the second as before, and the matrix product is formed as usual by summing over...
50. ### Fortran Permutation of indices in fortran

Hi there. I am working with a numerical quadrature in some scheme to solve a set of equations. At this point I am working in two dimensions. The thing is that I have some function ##\psi_m(x,y,\Omega_m)## with ##\Omega_m=(\Omega_{x,i},\Omega_{y,j})## with ##\displaystyle...