Klein Definition and 107 Threads

Calvin Richard Klein (born November 19, 1942) is an American fashion designer who launched the company that would later become Calvin Klein Inc., in 1968. In addition to clothing, he also has given his name to a range of perfumes, watches, and jewellery.

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  1. M

    Klein bottle in 4d- Questions/ Discussion

    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...
  2. L

    Klein Gordon & spacelike/timelike virtual photon

    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...
  3. L

    Klein 4-group 2 Associative property

    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##...
  4. L

    Proof: Proving Klein 4 Group is Not Isomorphic to ##Z_4##

    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...
  5. J

    Can a Klein Bottle Manifold Describe Certain Mechanical Systems?

    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...
  6. S

    Solutions of the free one-particle Klein Gordon equation

    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...
  7. S

    Green's function & Klein Gordon

    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...
  8. S

    Time Dependent Perturbation Theory - Klein Gordon Equation

    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 +...
  9. A

    Help probability amplitud Klein gordon

    Homework Statement Hello, I need help. I don't know how to calculate this expression. probability amplitude in the final state of antiparticle with momentum q and particle with momentum p. I should write it in terms of creator and anihilation operators...
  10. L

    Constructing a Solid Klein Bottle

    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...
  11. F

    Conformal Invariance Klein Gordon Action

    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...
  12. arivero

    Higgs, SuperStrings and Kaluza Klein

    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...
  13. L

    Calculating the Z2 cohomology of the Klein Bottle using intersections

    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...
  14. JeremyEbert

    What is the Klein Four-Group Geometry and Its Applications?

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

    How to construct the two sheet cover of Klein Bottle?

    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!
  16. Spinnor

    With Kaluza Klein theory can electric field lines thought of differently?

    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!
  17. N

    Klein Gordon equation and particles with spin

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

    How can you drive the metric of kaluza klein in 5 D?

    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
  19. O

    Klein Gordon eqn, decoupling degrees of freedom

    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...
  20. K

    Automorphism group of Klein four is S3.

    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...
  21. G

    The Klein Paradox - Exploring Beyond the Negative Coefficient of Transmission

    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...
  22. L

    Equations for the Lawson Klein Figure

    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...
  23. O

    Charge conjugation of Complex Klein Gordon Lagrangian

    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...
  24. M

    Klein bottle as the union of two Mobius bands

    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...
  25. L

    Proving the Hamiltonian Operator in QFT with Klein Gordon Lagrangian

    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...
  26. B

    Solution to the Klein Gordon Equation

    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...
  27. O

    Christoffel connection in Kaluza Klein Theory

    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}...
  28. R

    Kaluza Klein, Goldstone Bosons, symmetries obliging masslessness?

    Kaluza Klein, Goldstone Bosons, symmetries obliging masslessness? Hello physics people, I hope all is well, and that everyones feeling festive even though i don't celebrate xmas lol! Iv got some weird questions, at least for me. Iv been working on Kaluza-Klein theory and have found weird...
  29. A

    Can a Klein Bottle be Constructed Using Rectangular Prisms and Circles?

    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...
  30. R

    Kaluza-Klein Theory: Unifying Weak Force and Gravity

    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...
  31. haushofer

    Non-relativistic limit of Klein Gordon (and massless limits)

    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...
  32. T

    How to compute the cohomology of the Klein bottle

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

    Kaluza Klein and gauge symmetry breaking.

    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...
  34. maverick280857

    Question about the Klein Gordon Propagator

    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...
  35. J

    Klein Paradox: Clarifying Concepts & Coefficients

    I've been doing quite a bit of reading on the Klein Paradox, though I have to admit a lot of the math goes over my head. So I was hoping you guys at PF could clarify a few things and help me check my conceptual understanding so far. I found this post...
  36. maverick280857

    Exploring the Meaning of Positive and Negative Energy in the Klein Gordon Field

    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.
  37. maverick280857

    Convergence of vacuum state of Klein Gordon field in a box

    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...
  38. maverick280857

    Expressing the Klein Gordon Hamiltonian in terms of ladder operators

    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...
  39. maverick280857

    How to solve the Klein Gordon Complex Field?

    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...
  40. quasar987

    Homology of the Klein Bottle using M-V sequences

    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...
  41. quasar987

    How do you get the Klein Bottle from two Möbius Strips?

    ...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...
  42. S

    Klein gordan equation in electromagnetic potential

    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...
  43. Hans de Vries

    The Lorentz force derived from the Klein Gordon equation

    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 Lorentz Force has a...
  44. N

    Find Generators and relations analogous to (2.13) for the Klein four group.?

    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.
  45. B

    Solving the Massless Klein Gordon Equation

    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...
  46. E

    News Can Edited Clips Create a True Debate Between Naomi Klein and Milton Friedman?

    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
  47. O

    Klein Gordon equation, probability density

    [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})...
  48. mbrmbrg

    Exploring Klein Bottles on the Web - Adventures of a Computer Lab Researcher

    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...
  49. M

    Galois and Klein 4: Isomorphic or Cyclic?

    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?
  50. I

    Is the Klein 4 Group on YouTube?

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