What is Connection: Definition and 516 Discussions
In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms.
Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of a coordinate frame, and so is not a tensorial object. Various generalizations and reinterpretations of the connection form were formulated subsequent to Cartan's initial work. In particular, on a principal bundle, a principal connection is a natural reinterpretation of the connection form as a tensorial object. On the other hand, the connection form has the advantage that it is a differential form defined on the differentiable manifold, rather than on an abstract principal bundle over it. Hence, despite their lack of tensoriality, connection forms continue to be used because of the relative ease of performing calculations with them. In physics, connection forms are also used broadly in the context of gauge theory, through the gauge covariant derivative.
A connection form associates to each basis of a vector bundle a matrix of differential forms. The connection form is not tensorial because under a change of basis, the connection form transforms in a manner that involves the exterior derivative of the transition functions, in much the same way as the Christoffel symbols for the Levi-Civita connection. The main tensorial invariant of a connection form is its curvature form. In the presence of a solder form identifying the vector bundle with the tangent bundle, there is an additional invariant: the torsion form. In many cases, connection forms are considered on vector bundles with additional structure: that of a fiber bundle with a structure group.
microwave radiation and the shape of the universe? The hotter parts could indicate parts of the universe that are closer to Earth while the colder parts could indicate the opposite, which would mean the universe is not a perfect geometric shape, which would show no variation in the cosmic...
I'm seeing lots of underlying connections between the canonical formulism of QFT and QM. But I'm getting a bit confused by their differences. I'll just write down my thought process:
QM is a one parameter system (t) in a space with three quantized operators (x,y,z)
QFT is a four parameter...
For a while I have wondered if the refraction of light had any connection to gravity on small scales (dare I say . . . quantum gravity?!?). I found this paper in the Cornell University Library. Below is the link and a copy of the opening synopsis that anyone can see without downloading it. . . ...
http://www.slideshare.net/viv3ksharma/automatic-school-bell
In this circuit I Think the emitter and collector terminal of the transistors T1 & T2 will be reverse. Otherwise the 555 timer will not discharge. Can anyone help pls?
In an automatic school bell circuit, The outputs from 3 to 11 are connected to the base of an NPN (BC547) transistor through 1K resistance. A diode is connected in forward bias in each of those outputs so that only one output sends high pulse to the base of the transistor. When the high pulse is...
The Double Slit Experiment & its Connection to "Pseudoscience"
Introduction
Hello everyone :), thank you for taking the time to view this as I have ALOT of questions regarding The Double Slit experiment and its connection to "The Law of Attraction" (LOA) or what many call pseudoscience. I...
Endorphins in the body act as chemical signals to the morphine-opium receptors (MOR) in the brain and morphine derivatives also react to this receptor. For example alpha-endorphin is a peptide with 10 amino acids and morphine has an aromatic 5-ring non-planer structure.
What set of...
Apologies for what may be a basic question, I am unfamiliar with RF systems but much more familiar with optics.
I need to connect some standard coax to some microcoax; they do not have exactly matching impedances so there are reflections. It seems to me I should be able to make an...
http://arxiv.org/abs/1306.4035
Graviton scattering amplitudes and Pure Connection Formulation of GR
Gianluca Delfino
(Submitted on 17 Jun 2013)
We show how the recently introduced "Pure Connection Formulation" of gravity provides a natural framework for approaching the problem of computing...
Hi everyone!
I have some problems with indices in general relativity. I am now working with the classic textbook by S. Weinberg and in eq. (4.7.4) we find...
This is a more a question about rules/regulations than actual EE, but I figured this was still the best sub-forum.
We are about to start renovating a house, and we will have to change a few things in the central heating system.
One problem is that we somehow need to get a cable from the wiring...
Hey
I have taken a programming course. And I have learned about Simpson, Trapezoidal and the midpoint rule etc, I have programmed these.
I have also implemented forward Euler, backward euler, Runge Kutta etc for solving ODE.
I am wondering if there is any way to unify these two things, are...
If we have a metric connection with no other restrictions (torsion may be non-zero), do the connection coefficients {\Gamma^{\alpha}}_{\mu\nu} have any symmetries among the indeces? I'm thinking not.
Or.. for a Levi-Civita connection, the only fixed symmetry condition is...
I recently discovered that for a 3rd degree polynomial I was studying, f(5) - 4f(4) + 6f(3) - 4f(2) + f(1) = 0. At first I just though it was coincidental that the coefficients were the 5th row of Pascal's Triangle, but then I tried a 2nd degree polynomial and found that f(4) - 3f(3) + 3f(2) -...
Hello everyone,
Can you guys please explain why a potentiometer needs a ground (-) wire? or what does it do differently and what uses there are for it as opposed to a rheostat.
Recently been playing around with automotive sensors like the TPS (Throttle Position Sensor) on a car and just...
I understand there is a connection, as there is time dilation due to gravity and also time dilation due to velocity. The formula for gravitational time dilation also looks very similar for the Lorentz factor used to calculate relativistic time dilation.
Is it because light is(in a sense)...
Is the remote desktop client in windows really bandwidth intensive?
We get roughly 16mb/s down and 1mb/s up even at fairly peak times, however as soon as dad goes on his laptop to use his desktop computer back at the office the internet becomes horribly slow, it doesn't seem to be a speed...
This question comes from trying to generalize something that it easy to see for surfaces.
Start with an oriented surface smoothly embedded in Euclidean space. The embedding determines two mappings of the unit tangent circle bundle into Euclideam space.
Given a unit length tangent vector,e, at...
While sitting contemplating life today, I had a thought. Naturally were connected to the earth...The civilizations throughout history had a much deeper profound connection to it as well. The only difference besides technological advances is we wear shoes with rubber soles...Rubber is not...
Hello, I am trying to hook up MATLAB to my arduino. I am trying to write a number to the serial port in the arduino IDE and retrieving the same number in the MATLAB IDE. My arduino code is:
void setup() {
// initialize serial communication at 9600 bits per second:
Serial.begin(9600);
}...
There are two railroads, represented by the curves y=(1/2)x2+7, and x2+y2=1. I am supposed to find a straight line connection so that a atrain can get from one curve to the other.
I have drawn a simple diagram to help me picture things:
http://i50.tinypic.com/2saeccx.png
where (a,b) and (c,d)...
(1,a^2,a^2,a^2)) from the action; \mathcal{S}_{D}[\phi,\psi,e^{\alpha}_{\mu}] = \int d^4 x \det(e^{\alpha}_{\mu}) \left[ \mathcal{L}_{KG} + i\bar{\psi}\bar{\gamma}^{\mu}D_{\mu}\psi - (m_{\psi} + g\phi)\bar{\psi}\psi \right]
I can show that, i\bar{\gamma}^{\mu}D_{\mu}\psi -...
In trying to derive the Dirac equation in space-time (1,-a^{2},-a^{2},-a^{2}), I have read that the Dirac equation is (i\bar{\gamma}^{\mu}(\partial_{\mu}+\Gamma_{\mu})-m)\psi=0 where,
\Gamma_{\mu}=\frac{1}{2}\sum ^{\alpha \beta}e_{\alpha}^{\mbox{ }\nu}(\frac{\partial}{\partial...
There is some theorem along the lines that any category of schemes embeds into a suitable Grothendieck topoi. What is the exact statement of this theorem?
I stumbled over something reading Green's Matrix Mechanics (1965) this afternoon. There was an equation very similar to one I saw in Dirac's Lectures on Quantum Field Theory (1966), where he talks about the equivalence (or near equivalence) of the Schrödinger and Heisenberg formulations of...
Hi
I am being told in "PBS NOVA 2013 Earth from space" that the Amason rainforest is being fed continously with phosphites from the Sahara desert where an ancient lakebed releases diatomites into the atmosphere.
All good and well - you might think. But wait! The same program, as well as...
So I recently moved houses and with it we were given a new modem. I had previously used a modem and my own (relatively expensive) router which worked wonderfully, but now, with this all in one modem+router they had given my family, the quality of our internet connection has noticeably dropped...
I know how, by Amp\grave{e}re's Law for the loop integral of a magnetic field, $$\oint_C \textbf B \cdot d \textbf s = \mu_0 I$$ and this is zero when there is no current enclosed in the loop; there is a nonzero result when there is a current.
With Cauchy's Integral Theorem, if a function is...
I am connecting my towers power wires to the motherboard.
The motherboard tells me how to connect the. Hdd led cable. And were the pluss and minus wires go.
But the. Hdd led cable is mad of a. Blue and white wire.
Witch one is the pluss. And. Negitive?
I understand that the indefinite integral is like infinite definite integrals, but how come when we calculate the definite integral we simply substitute the two values into the indefinite integral and subtract? Why do we subtract? Why not add?
Also, there aren't the same thing, right? What's...
Hi,
I'm trying to understand the fiber bundle formulation of gauge theory at the moment, and I'm stuck on the connection. Every reference I've found introduces the idea of a connection on a principle bundle as a kind of partitioning of the tangent space at all points in the total space into a...
Does anyone have a good book or reference on computing riemannian connections. I'm looking at Do Carmo and can't find any examples. For ex. If X = y(d/dx) + x(d/dy) + w(d/dz) -z(d/dw), Y = z(d/dx) - w(d/dy) - x(d/dz) + y(d/dw), Z = w(d/dx) + z(d/dy) - y(d/dz) - x(d/dw) being the classical...
My wife has an ASUS laptop K53E series Notebook running Windows 7 Home Premium which she bought to use at her work (she is a teacher), the school part purchased with her and had the school IT set up everything.
The problem started when the school IT wonk set up the WIFI to connect to the school...
My understanding is that (definite) integration defines area in R^2, volume in R^3 etc, and my question is: would calculating an area in R^2 using integration give the same answer as counting the unit squares. If so, how did they ensure to define integration in such a way as to give the same...
I work in valve manufacturing business, I have posted some questions on designs of pins before. Here is one I would like verified.
In a 400mm pinch valve I have the driving spindle fastened to the top pinch bar through a M36x4 thread. To secure the thread a drilled a hole and fitted a smaller...
What is the connection between QM and classical mechanics? This has never been obvious to me, but it seems that it would be desirable that we should be able to derive the laws of CM from QM, but I've never really seen that done convincingly. Can you actually show that a very large quantum system...
I need help with Part (b). I finished part (a) and attached it as well. My issue comes from how to apply the definition of connection forms to compute them. The definition states: Let E_1, E_2, E_3 be a frame field on R^3. For each tangent vector v at R^3 at the point p let \omega_{ij}(v )=...
Hi all;
i would like to establish a wireless connection on my Scientific Linux 6.3 on my laptop
the wired connection is well established
anyone help me ?
Hello,
We've recently decided that our energy monitors need to be reseted; to do so we need to connect to the devices as this can't be done from their menu (https://www.gavazzionline.com/pdf/EM2172DDS.pdf this is the meter).
In order to connect we've acquired an RS485>RS232 converter...
Very cool! I just started using my new femtocell connection from AT&T. It provides a cell connection for a range of about 10 meters, using an internet connection. It seems to work great. The connection is solid with 5 bars, and the sound quality is excellent.
I have been playing dueling phones...
Okay i know that energy is the ability or capacity to do work. But how do you define work, as like the isn't work just the transference of energy in one form to another? Which is kinda circular reasoning. Like the rely on each other for a defintion. Is that right?
Hi guys,
If we connect 2 Dc generators in parallel. First generator ratings (200 V, 400 Amp),and the
second Generator (400 V, 500 Amp). What are the output voltage and the max.output current?
What if we connect them in Series ?
What if these generators are Ac generators?
Hi
I'm working on a way of connecting prismatic LiFePo4 pouch cells into a battery pack.
I'll probably use G10/FR4 for the isolators, as suggested by MQuack in the Mechanical section of this forum, see this animation (the green parts are the FR4...
Is it possible to have a fiber optic wire spliced onto another (or starting from 3 separate fibers) to form a Y shape and have loss-less (or close thereto, as good as a normal splice) transmission from 2 of the fibers into the third? I know this wouldn't work for double-clad fiber or for...
Homework Statement
Hello, let me introduce myself first. I am Wira, a Senior High School alumnus in Indonesia. I am currently preparing for my university entrance exam. This is a problem which I get stuck in, and can you help me with it?
Indonesian:
Suatu mesin kalor yang bekerja dengan siklus...
My physics book explains that this is because of the conservation of charge and the fact that charge doesn't accumulate at a certain point.
Can someone please explain this in detail, especially the part where it says that charge can't accumulate.
Another question which i think is similar is...