Symbols Definition and 294 Threads

I suspect that phonetic spelling is done using different systems. Briefly trying a search on internet, I am not finding the exact symbols I am looking for and some of what I want do not seem to be found in Windows Character Map. I feel a little lost. I can come-up with something that may...

This is from Giancarlo Bernacchi's book "Tensors made easy": And this is from Daniel Fleisch's book "A Student's Guide to Vectors and Tensors": The meaning of the two lower indices is exchanged in the two explanations. Is one of them correct and the other one wrong, or is there no consensus...

TL;DR Summary: Looking for downloadable package of symbols Hi; I am picking up on the suggestion of using LAtex. I know the symbols are mostly in Word scattered about the place. Is there a downloadable package do you know that I could access please. Thanks Martyn

Some may say that ##\frac{ \partial g }{ \partial t }## is correct because it is a term in a partial differential equation, but since ##g## is a one variable function with ##t## only, I think ##\frac{ dg }{ dt }## is correct according to the original usage of the derivative and partial...

About a month or two ago I started doing simulations of light physics around black holes and yesterday I got a fast Christoffel symbols function for the Schwarzschild metric in cartesian coordinates, but now the photon ring appears flipped. I feel as though it is wrong. But as I am still pretty...

The Hiscock coordinates read: $$d\tau=(1+\frac{v^2(1-f)}{1-v^2(1-f)^2})dt-\frac{v(1-f)}{1-v^2(1-f)^2}dx$$ ##dr=dx-vdt## Where ##f## is a function of ##r##. Now, in terms of calculating the christoffel symbol ##\Gamma^\tau_{\tau\tau}## of the new metric, where ##g_{\tau\tau}=v^2(1-f)^2-1## and...

Since ## p=73 ## in this problem, how should I prove that ## \sum_{r=1}^{73-1}r(r|73)=0 ##? Given that ## 73=1\pmod {4} ##.

My brother is a gene scientist and wants a piece of art that contains the symbols of the four nucleotides ACGT. He described the symbols as "really nothing more than the benzene ring with a bump in certain places". What is the simplest possible way to symbolically represent them? (i.e. short...

"the christoffel symbols are all zero at the origin of a local inertial frame" Why must it be at the origin? If it is not?Thanks!

Hi, Suppose I am given a sequence of special symbols and I want to produce the next sequence of symbols according to certain rules that transform one symbol into one or more symbols. They are 10 symbols in total, say; A, B, C, D, E, F, G, H, I, J The rules are: A transformed into B and it is...

Hey guys! I'm looking at a few resources and I came across an interesting one on the Aviation Stack Exchange Page. Interestingly enough, another individual is working on implementing flight mechanics / aerodynamics using code and had similar questions to me, but to be honest, I'm not quite sure...

I've seen quite a few websites but I don't know how far to trust them. Is there a book I could use? Thanks so much Joe

M. Blennow's book has problem 2.18: Show that the contracted Christoffel symbols ##\Gamma_{ab}^b## can be written in terms of a partial derivative of the logarithm of the square root of the metric tensor $$\Gamma_{ab}^b=\partial_a\ln{\sqrt g}$$I think that means square root of the determinant of...

I have struggled for a long time to understand the difference between the meaning of the concept of 'equality' and 'identity' as represented by the symbols ##=## and ##\equiv##. Can someone explain it to me and give examples where ##=## does apply and ##\equiv## does not and vice versa?

The axioms: My work: Extension:$$\forall x\forall y,\,(x=y)\iff(\forall z,\,(z\in x\iff z\in y))$$ Empty Set:$$\exists x|\forall y,\,\neg(y\in x)$$ Pair Set:$$\forall c\forall d,\,\exists e|(c\in e)\wedge(d\in e)\wedge[\forall f,\,\neg((f=c)\vee(f=d))\implies\neg(f\in e)]$$ If you consider any...

I love the Sixty Symbols you tube videos. But I'm curious, does anyone know who the whiny-voiced guy who sometimes asks off-screen questions is? Thanks.

If I want to calculate ##\tilde{\Gamma}^\lambda_{\mu 5}##, I will write \begin{align} \tilde{\Gamma}^\lambda_{\mu 5} & = \frac{1}{2} \tilde{g}^{\lambda X} \left(\partial_\mu \tilde{g}_{5 X} + \partial_5 \tilde{g}_{\mu X} - \partial_X \tilde{g}_{\mu 5}\right) \\ & =\frac{1}{2}...

I am trying to find $$\Gamma^{\nu}_{\mu \nu} = \partial_{\mu} log(\sqrt{g})$$ but I cannot. by calculations, I manage to find $$\Gamma^{\nu}_{\mu \nu} = \frac{1}{2}g^{\nu \delta}\partial_{\mu}g_{\nu \delta}$$ and from research I have find that $$det(A) = e^{Tr(log(A))}$$ but still I cannot...

Can you approach the GR two body problem through summations of multiple Schwarzschild solutions? Specifically, by using the Schwarzschild metric for each body of mass, then adding the Christoffel symbols together, to arrive at a new geodesic equation. Take point C between bodies A and B...

Is a connection the same thing as a covariant derivative in differential geometry? What Is the difference between a covariant derivative and a regular derivative? If you wanted to explain these concepts to a layperson, what would you tell them?

Actually I know there would be some permutations used here. I know how to calculate the symbols but estimating is quite a new thing to me

E very once in a while I see a post in which LaTex symbols appear that are absent from the primer offered in PF. Examples: \bf A in lieu of the awkward \mathbf A ## \ell ## for script l. There must olbviously be a list of the 28 letters that can be scripted. The font section in my LaTex...

I don't have a clue as to how to go about proving (or verifying) the equation above. It would be very hard to take individual values of i,j and k and p,q and r for each side and evaluate ##3^6## times! More than that, I'd like a proof more than a verification. Any help would be welcome.

I am using the code provided by Artes here, but I am missing something. The Chrisfoffel-symbol formula is $$\Gamma^{\mu}_{\phantom{\mu}\nu\sigma}=\frac{1}{2}g^{\mu\alpha}\left\{\frac{\partial g_{\alpha\nu}}{\partial x^{\sigma}}+\frac{\partial g_{\alpha\sigma}}{\partial x^{\nu}}-\frac{\partial...

I am trying to create a function to calculate the Christoffel Symbols of a given metric (in this case the Shwartzchild metric). Calculating the (non zero) Christoffel Symboles for the Shwartzchild connection, I am a double major in Physics and Computer Science so I decided to go the code rout...

My notes seem to imply this should be obvious : If i consider the covariant deriviative then i get something like christoffel= nabla ( cov derivative ) - partial So difference of two of them will stil have the partial derivatuves present ,assuming these are labelled by a different index ...

##\hat{r}_{\perp}## and ##\hat{r}_{\parallel}## How do "practicing" physicists and mathematicians verbalize these symbols? If they ever do? Do I say r-hat-perpendicular and r-hat-parallel?

What is difference between 1. kind Cristoffel symbol and 2. kind Cristoffel symbol? Is the Cristoffel symbol in ricci curvature tensor 1. kind or 2. kind?

Given : A) primitive symbols : (1, *) and B) The axioms: 1) \forall x\forall y[x*=y*\Longrightarrow x=y] 2) \forall x[x*\neq 1] 3) [P(1)\wedge\forall x(P(x)\Longrightarrow P(x*))]\Longrightarrow\forall xP(x) Then prove: \forall x[x=1\vee \exists y(y*=x)]

Hi All Given that the Riemann Curvature Tensor may be derived from the parallel Transport of a Vector around a closed loop, and if that vector is a covariant vector Having contravariant basis The calculation gives the result Now: Given that the Christoffel Symbols represent the...

I have a technical problem. 1. Accordingly to historical E.B. Christoffel’s work (I think year 1869), (Christoffel’s) symbols are symmetric in the two (today writing) lower indices. 2. These symbols have been introduced when studying the preservation of differential forms of degree two. The...

In Landau Book 2 (Classical Field Theory & Relativity), he mentions that the transformation rules of the christoffel symbols can be gotten by "comparing the laws of transformation of the two sides of the equation governing the covariant derivative" I would believe that by the equations...

{1, 2 ,3} = {1, 2, 3, 3, III}? {1, 2 ,3} = {one, dos, three}? {Tom, Dick, Harry} = {Thomas, Richard, Harrison}? Seems to me, these are undetermined until the set's "type" or "category" definition of its members is defined so as to determine what elements are members of the set... whether...

I've noticed that for both the surface of a sphere and a paraboloid, one arrives at the same Christoffel symbols whether using \Gamma^i_{kl} = \frac {1}{2} g^{im} ( \frac {\partial g_{mk} }{\partial x^l} + \frac {\partial g_{ml}}{\partial x^k} - \frac {\partial g_{kl}} {\partial x^m} )...

What is the general difference or importance between using christoffel symbols of the first kind and those of the second kind in terms of geometry and their application. The christoffel symbols of the second are identical to those of the first except with the inverse metric tensor in front...

So I'm trying to get sort of an intuitive, geometrical grip on the covariant derivative, and am seeking any input that someone with more experience might have. When I see ##\frac {\partial v^{\alpha}}{\partial x^{\beta}} + v^{\gamma}\Gamma^{\alpha}{}_{\gamma \beta}##, I pretty easily see a...

There are some pictures in Nielsen's book that I find confusing: Why there is a line half-crossing the X-box? Similarly, why there is a line connecting to ##f \left ( x \right )##? There are two H gates between ##\left | \psi _0 \right >## and ##\left | \psi _1 \right >##. Why one of them has...

First, I want to be pedantic here and underline the distinction between a set (in the model, or interpretation) and a sentence (in the theory) which is fulfilled by that set, and also constant symbols (in the theory) versus constants (in the universe of the model) Given that, I would like to...

I don't know how to type mathematical symbols and equations and stuff. Like if I want to ask something here in physics forum, I need to type mathematical expressions like everyone here does. How can I do that? Do I need any software?

In Micheal O. Searcoid's book "Elements of Abstract Analysis" we read the following: Help will be much appreciated ...Peter ========================================================================== It may help readers of the above post to hve access to Searcoid's text of Definition 1.3.4 ...

I need to find all the non-zero components of the Riemann Tensor in a two-dimensional geometry knowing that the only two non-zero components of the Christoffel symbols are: \Gamma^x_{xx}=\frac{1}{x} and \Gamma^y_{yy}=\frac{2}{y} knowing that: R^\alpha_{\beta\gamma\delta}=\partial_\gamma...

Hi! I'm asked to find all the non-zero Christoffel symbols given the following line element: ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy The result I have obtained is that the only non-zero component of the Christoffel symbols is: \Gamma^x_{xx}=\frac{1}{x} Is this correct? MY PROCEDURE HAS BEEN: the...

Let the metric be defined as ##ds^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2## Through some calculations, we then see that our connection one forms are ##\omega_{12} = -d \theta## and ##\omega_{21}= d\theta##, ##\omega_{13} = -sin\theta d \phi## and ##\omega_{31} = sin\theta d\phi##...

Hello everyone, I'm sure a lot of you know that the Christoffel symbols are not tensors by themselves but, their variation is a tensor. I want to revive a post that was made in 2016 about this: The Variation of Christoffel Symbol and ask again "How is that you can calculate ∇ρδgμν if δ{gμν} is...

Homework Statement Given some 2D line element, ## ds^2 = -dt^2 +x^2 dx^2 ##, find the Christoffel Symbols, ## \Gamma_{\beta \gamma}^{\alpha} ##. Homework Equations ## \Gamma_{\beta \gamma}^{\alpha} = \frac {1}{2} g^{\delta \alpha} (\frac{\partial g_{\alpha \beta}}{\partial x^\gamma} +...

Can anyone help? What is the convention for inserting the vector symbol? I have a draft with -(\vec{2.5})^2 which displays correctly in preview ##-(\vec{2.5})^2\\## why is vec troublesome and underlined in red?? Should I ignore! I realize that I'm not using a variable.

Hi, in some books the ##\nabla## symbol is used for the Laplacian ##\frac{d}{dx^2}+\frac{d}{dy^2}+\frac{d}{dz^2}## while others use the ##\Delta## symbol for this. What is the correct custom for this usage?

I have a couple of questions about how Christoffel symbols work. Why can they just be moved inside the partial derivative, as shown just beneath the first blue box here: https://einsteinrelativelyeasy.com/index.php/general-relativity/61-the-riemann-curvature-tensor And if you had the partial...

I wish to display symbols like < and > as in < z_n > but more like the symbols in the following text ... Hope someone can help ... Peter

So I'm currently doing a project on motors. It just so happens that I'm dealing with both electrical current and rotational inertia. I have one small problem. The symbol for electrical current is I. But so is rotational inertia! Are there any other symbols for rotational inertia/electrical...