Klein Definition and 104 Threads

Before I get down to business, I would like to note (you don't have to read this; feel free to skip to where it says "here are my questions") the following: ------------- Firstly, I am somewhat still new to posting in these forums, and as such, am not sure if this is the right place to put this...

Homework Statement See attachment. Homework Equations The Attempt at a Solution So I have shown that the plane wave sol'n satisfies the Klein-Gordon equation by subbing in and reducing the equation to: E^2 = p^2c^2 + m^2c^4 which reduces to: E = pc for an m = 0...

Homework Statement How to prove in the easiest way that Klein 4-group is associative. Homework Equations Four elements ##a^2=b^2=c^2=e^2=e##. The Attempt at a Solution If that is group with four elements, how many types of ##a*(b*c)=(a*b)*c## I need to have? 1) ##e*(e*e)=e*e=e##...

Homework Statement Prove that Klein 4 group is not isomorphic with ##Z_4##. Homework Equations Klein group has four elements ##\{e,a,b,c\}## such that ##e^2=e,a^2=e,b^2=e,c^2=e## As far as I know ##Z_4## group is ##(\{\pm 1,\pm i\},\cdot)##. Right? The Attempt at a Solution As far...

Hi Yesterday during a lecture the Klein Bottle manifold was mentioned. We've been busy with describing the natural way of conducting mechanics on manifolds for a while now. Does anybody know how an example of a mechanical system which is described by a klein bottle manifold? I've been...

In the book "Wachter, relativistic quantum mechanics", in page 5, the KG eq. is introduced as follows: -\hbar^2 \frac{\partial^2 \phi(x)}{\partial t^2} = (-c^2 \hbar^2 \nabla^2 + m^2_0 c^4) \phi(x). Now I tried to solve this equation using the separation ansatz (product ansatz). I get...

Hello, I was wondering what the use in the Green's function for the Klein-Gordon equation was, I have listed it below: \int \frac{d^4p}{(2\pi)^4}\frac{i}{p^2-m^2}e^{ip\cdot(x-x')} We find this gives an infinite result when the Klein gordon equation is applied to it and if x=x', what...

Hey, I'm struggling to understand a number of things to do with this derivation of the scattering amplitude using time dependent perturbation theory for spinless particles. We assume we have some perturbation 'V' such that : \left ( \frac{\partial^2 }{\partial t^2}-\triangledown ^2 +...

can one construct a solid Klein bottle - a 3 manifold whose boundary is a Klein bottle as follows. - Start with a solid cylinder and identify the two bounding disks by a reflection. - The boundary becomes a Klein bottle but is this a smooth manifold whose boundary is this Klein bottle? - If...

Wald Appendix D talks on why g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}\phi is not conformally invariant when n is not equal to 2. I want to prove that the Klein Gordon Action (V=0) is not conformally invariant. However the term that I have in the action is just...

13D "S-Theory" M4 x S9 has as isometry group SO(10) for the internal S9 space. 12D "F-Theory" M4 x S5 x S3 has SO(6)xSO(4), locally SU(4)xSU(2)xSU(2) 11D "M-Theory" M4 x ((S5xS3)/S1) has isometry group SU(3)xSU(2)xU(1) 10D is target space of SuperStrings, and perhaps also of Connes Chamseddine...

This thread asks for help calculating the Z2 cohomology ring of the Klein bottle using intersections. This is what I think. View the Klein bottle as a circle bundle over a circle. A fiber circle and the base circle generate the first Z2 cohomology by transverse intersection. - The fiber...

I think this a map of the Klein four-group geometry. Comments? http://dl.dropbox.com/u/13155084/prime-%20square-klein%20four%20group.png

How to construct the two sheet cover of Klein Bottle?? Dear Folks: There are four kinds of two sheet cover (up to homeomorhism) of Klein Bottle, it is easy to check torus is one of them, what are the others?? Many thanks!

Does Kaluza Klein theory allow one to think of the electric field lines of a point charge or a dipole differently. Is there any insight as to the nature of those field lines? Thanks for any help!

I am a newbie to QM. Why can't the Klein Gordon equation be used to describe particles with spin? Thanks

in many research of kaluza klein theory to unified electromagnetic & gravity fields these research begin with 5D metric how can i drive this metric? please any research drive this metric show me. note russian research's by english is very good if you know it show me . please it is very important

Having some trouble following my notes in QFT. Any help greatly appreciated. We have the Klein Gordon equation for a real scalar field \phi\left(\overline{x},t\right); \partial_{\mu}\partial^{\mu}\phi + m^{2}\phi = 0. To exhibit the coordinates in which the degrees of freedom decouple...

Homework Statement Show that \text{Aut}_{\text{Grp}}(\mathbb Z /2 \mathbb Z \times \mathbb Z /2 \mathbb Z) \cong S_3 . That is, show that the automorphism group of the Klein four group is the symmetric group on 3-letters. The Attempt at a Solution I think the argument here is pretty...

The Klein Paradox is the name given to the following prediction of Klein Gordon's equations. If you send a current of electrons against a potential barrier of height V such that the energy of the incident electrons is less then V - m, you should observe a current of positrons coming out of the...

Hi, Does anybody know the equations for the Lawson Klein bottle ? I am trying to construct it in a maths graphic application. Just to be precise its the version of the Klein bottle that is composed of two Sudanese Mobius bands, also it may be that the application will only cope with...

Homework Statement Show that the complex Klein-Gordon Lagrangian density: L=N\left(\partial_\alpha\phi^{\dagger}(x)\partial^\alpha\phi(x)-\mu^2\phi^{\dagger}(x)\phi(x)\right) is invariant under charge conjugation: \phi(x)\rightarrow C\phi(x)C^{-1}=\eta_c \phi^\dagger (x) Where C...

I am trying to calculate the homology groups of the Klein bottle. I want to use the Mayer-Vietoris sequence with the Klein bottle decomposed as the union of two Mobius bands (A and B which are homotopic equivalent to circles), now AUB is the Klein bottle, but I don't understand how according to...

The Hamiltonian operator in quantum field theory (of Klein Gordon Lagrangian) is H=\frac{1}{2} \int \frac{d^3p}{(2 \pi)^3} \omega_{\vec{p}} a_{\vec{p}}^\dagger a_{\vec{p}} after normal ordering Now we construct energy eigenstates by acting on the vacuum |0 \rangle with a_{\vec{p}}^\dagger...

Hey guys, I was reading up on the Klein Gordon equation and I came across an article that gave a general solution as: \psi(r,t)= e^i(kr-\omegat), under the constraint that -k^2 + \omega^2/c^2 = m^2c^2/\hbar^2, forgive my lack of latex hah. Through Euler's law this does give a solution...

Now I'm just start to study the Kaluza-Klein theory from http://arxiv.org/abs/grqc/9805018. I try to calculate the Einstein Field equations in 5 dimensional vacuum space-time. we start with 5D metric tensor, \hat{g}_{AB}=\begin{pmatrix}...

Hi guys. I'm doing a high school project for AP Calc BC. We're supposed to build a 3-D solid using Riemann approximations. Basically, we have to build an object using solely rectangular prisms, or circles. Prompt: Make a physical model of a solid with a known cross-section. For example, let's...

Hello everyone! Im new on this forum, have been lurking around paying attention to all the interesting stuff you guys talk about, and now iv joined up! Firstly, I am not sure if I am posting in the right place - there isn't really a distinct place for a question like this. Hopefully I am...

Hi, I have a conceptual question about taking non-relativistic (NR) limits of the Klein-Gordon equation, inspired by Zee's book on QFT (chapter III.5) So we have a complex scalar field with the equation of motion (\partial^2 + m^2 ) \phi = 0 Then we consider the fact that \phi \sim...

Using the Mayer–Vietoris sequence, how can we calculate the De Rham cohomology of the Kelin bottle?

In standard, old-fashioned, Kaluza Klein theory we have new dimensionful parameters, the size of the compact dimensions, but they become dimensionless after quotient against the Plank size, so they become the adimensional coupling constants of the gauge groups associated to the symmetry of the...

Hi, I'm teaching myself QFT. I don't understand some of the calculations described on pages 29 and 30 of Peskin and Schroeder's book on QFT. The next step is where I have a problem I think I'm making a mathematical mistake somewhere, but I haven't been able to figure it out yet. Making a...

Hi everyone The Hamiltonian of the Klein Gordon field can be written as H = \frac{1}{2}\int d^{3}E_p \left[a^{\dagger}(p)a(p) + a(p)a^{\dagger}(p)\right] and we have [H,a(p')] = -E_{p'}a(p') [H,a(p')] = +E_{p'}a^{\dagger}(p') The book I'm reading states that What does this mean? Thanks.

Hi I've been reading through the book "Quantum Field Theory: A Tourist Guide for Mathematicians" by George B. Folland. On page 101, he describes the construction of a scalar field "in a box" \mathbb{B}: \left[-\frac{1}{2}L,\frac{1}{2}L\right]^3 in \mathbb{R}^3. Here \bf{p} lies in the...

Hi everyone I'm trying to express each term of the Hamiltonian H = \int d^{3}x \frac{1}{2}\left[\Pi^2 + (\nabla \Phi)^2 + m^2\Phi^2\right][/tex] in terms of the ladder operators a(p) and [itex]a^{\dagger}(p). This is what I get for the first term \int d^{3}x...

Hi I am teaching myself QFT, and this is not a homework problem. Right now, I am learning Classical Field Theory, and I am not sure how to proceed with the following problem. I would be grateful to receive inputs and suggestions. Problem Given the Klein Gordon Lagrangian with a complex...

About the proof of the homology of the Klein Bottle here: http://en.wikipedia.org/wiki/Mayer%E2%80%93Vietoris_sequence#Klein_bottle. I do not see how the conclusion follows from the fact that we can "choose" {(1,0), (1,-1)} as a basis for Z²...

...as in the little poem A mathematician named Klein Thought the Möbius band was divine. Said he: "If you glue The edges of two, You'll get a weird bottle like mine. That can be found in the wiki page about the Klein bottle...

Its troubling me a lot that when we start solvingK.G. equation for a free particle we assume energy as a sum of nonrelativistic energy and mc2. but when it is tried to solve the equation for a particle in electromagnetic field we solve it without taking into account the term mc^2. for reference...

[SIZE="3"][FONT="Arial"] The Lorentz Force and Maxwell's equations derived from Klein Gordon's equation . http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdfI posted several new chapters of my book lately, mostly involving the Klein Gordon equation. This chapter shows how the...

Find Generators and relations analogous to (2.13) for the Klein four group.? (2.13) i^4=1, i^2=j^2, ji=(i^3)j. (a) Find Generators and relations analogous to (2.13) for the Klein four group. (b) Find all subgroups of the Klein four group. Please show steps! Thank you.

I am being really thick here I have this wave equation, the massless klien gordon equation \partial_{\mu}\partial^{\mu}\phi(x)=0 where the summation over \mu is over 0,1,2,3 the general solution is a superposition of plane waves yes? i.e \phi(x)=\int d^4 p...

Great video, where someone puts various clips of Naomi Klein's and Milton Friedman's in order to simulate a debate between the two. http://cafehayek.typepad.com/hayek/2008/01/naomi-vs-milton.html

[SOLVED] Klein Gordon equation, probability density Homework Statement Use the Klein-Gordon Equation to show that \partial_{\mu}j^{\mu} = 0 Homework Equations KG: \left(\frac{\partial^{2}}{\partial t^{2}} - \nabla^{2} + m^{2}\right) \phi = (\partial_{\mu}\partial^{\mu} + m^{2})...

I was looking up möbius strips online, and naturally wandered into klein bottle territory, and ended up at http://www.kleinbottle.com/" . It's reading week, and I'm in the university's computer lab. Heaven protect me if an overworked English Major comes over and asks why I'm disturbing the...

suppose a +ve degree polynomial g(x) in G[x] with F splits over G and no irr. factor has repeated root. then if [F:G]=4, we know the size of Gal(F/G) is also 4. so it's either isomorphic to the Klein 4 or cyclic group of order 4. is there any trick to tell it's one and not the other?

http://youtube.com/watch?v=UTby_e4-Rhg

Suppose that we take the Klein-Gordon Hamiltonian to be of the form H = \int d^3x \, \mathcal{H}(x) = \frac{1}{2}\int d^3x\, (\pi^2(x) + (\nabla\phi(x))^2- m^2\phi^2(x)) If we want to compute, say, the evolution equation for \phi(x) we use the Poisson bracket: \dot{\phi}(x) = \{\phi(x),H\} =...

When searching for KK stuff in forums, I see that when g(5) is applied to L(5 R), this effectively splits the equation of motion into a (4) gravitational part, (4) electromagnetic part and the Plank mass associated with a miniscule x^5. I have no problem accepting that GR can do this and calling...

I went off on my own to study the Euler caracteristic + orentability caracterisation of closed surface and I must have gotten lost somewhere, because I do not find that the Klein bottle is homeomorphic to \mathbb{R}P^2\#\mathbb{R}P^2 as I should. I started with the result that for two surfaces...