Klein Definition and 104 Threads

Hello. I'm going over some old uni notes, and I'm hoping to learn a bit more about categories and things like fibrations. But in 3rd year, we looked at the Klein 4-group. I know of two examples, one where I can have an additive V4 acting on pairs of two-way crossbar switches, in what I suppose...

Here's your text with the changes you requested: The Kaluza-Klein metric, by reduction, can be written as a ##(4+m) \times (4+m)##symmetric matrix, where ##m## is the dimension of the additional spacetime (if we decompose ##M_D = M_4 \times M_m##). It was show by Bryce de. Witt that, if the...

https://www.uni-math.gwdg.de/aufzeichnungen/klein-scans/klein/ I hope you enjoy folks. It would be nice to see an English translation somewhere. Same for his encyclopedia.

I want to get the stress energy tensor of a scalar field using the Hilbert method (namely, ##T^{\mu v} = \frac{2}{\sqrt{-g}} \frac{\delta S}{\delta g_{\mu v}}##) $$S = \int \frac{1}{2}(\partial_\mu \phi \partial^{\mu} \phi - m^2 \phi ^2)\sqrt{-g}d^4x$$ $$= \int \frac{1}{2}(\partial^{v} \phi...

Hello! I'm starting to study curved QFT and am slightly confused about the invariance of the Klein Gordon Lagrangian under a linear diffeomorphism. This is $$L=\sqrt{-g}\left(g^{\mu\nu}\partial_\mu \phi \partial_\nu \phi-\frac{m^2}{2}\phi^2\right),$$ I don't see how ##g^{\mu\nu}\to...

Klein Gordon Lagrangian is given by \mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^2\phi^2 I saw also this link https://www.pas.rochester.edu/assets/pdf/undergraduate/the_free_klein_gordon_field_theory.pdf Can someone explain me, what is...

As $$\hat{P_i} = \int d^3x T^0_i,$$ and $$T_i^0=\frac{\partial\mathcal{L}}{\partial(\partial_0 \phi)}\partial_i\phi-\delta_i^0\mathcal{L}=\frac{\partial\mathcal{L}}{\partial(\partial_0 \phi)}\partial_i\phi=\pi\partial_i\phi.$$ Therefore, $$\hat{P_i} = \int d^3x \pi\partial_i\phi.$$ However...

I have a question about the Klein paradox in the massless case, for a potential step of height ##V_0## (this is exactly the situation described by Wikipedia). I don't have a problem to understand the "paradox", and I think the Wikipedia's illustration is quite telling. My question is : what...

From Wikipedia: Which should be conceptually similar of what happen in the non-relativistic limit of the Dirac equations when you see that the solutions decouple. Do you have any reference that I can look up where the derivation for the KG field is performed? Thanks in advance!

The correct answer is: #P = \int \frac{dp^3}{(2\pi)^3}\frac{1}{2E_{\vec{p}} \big(a a^{\dagger} + a^{\dagger}a\big)# But I get terms which are proportional to ##aa## and ##a^{\dagger}a^{\dagger}## I hereunder display the procedure I followed: First: ##\phi = \int...

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}...

What is the spin one Klein Gordon Equation? What is the formula for the conserved current, i.e. the electric current density four-vector?

What problem actually arises when we take the second order time derivative in KG equation

Let us suppose we have a scalar field ##\phi##. The Klein-Gordon equations for the field can be written as \begin{equation} \ddot{\phi} + 3H \dot{\phi} + \frac{dV(\phi)}{d\phi} = 0 \end{equation} The other two are the Friedmann equations written in terms of the ##\phi## \begin{equation} H^2 =...

In theory, does an algebraic expression exist for the ground state of the Klein Gordon equation with \phi^4 interactions in the same way an algebraic expression exists for the simple harmonic oscillator ground state wavefunction in Q.M.? Is it just that it hasn't been found yet or is it...

The left side of the equality of ##(5)## is obvious from ##(4)##, however the rest of the terms are still unknown to me. I have tried adding and subtracting terms similar to the rest of the terms so as to produce a commutator and use ##(3)##, but I can't seem to figure out how to get ##(5)##...

Homework Statement i need a detailed solution for Classical field Klein gordon equation please , i just stop when the delta function get evolved in Homework Equations The Attempt at a Solution

Homework Statement Show that Eq. (6.33) follows from Eq. (6.32) by changing variables from t to ##\eta##. Homework Equations (6.32) $$\frac{d^2\phi^{(0)}}{dt^2}+3H\frac{d\phi^{(0)}}{dt}+V'=0$$ (6.33) $$\ddot{\phi^{(0)}}+2aH\dot{\phi}^{(0)}+a^2V'=0$$ The Attempt at a Solution So...

A three dimensional figure, similar to the Klein Bottle. The Torbus Cup is made with two Torbus Rings counter-rotated that are single-sided with one edge morphed, similar to the connecting ends of Mobius Strip, The Torbus Ring is made by folding a Cornu-type geometry.

I'm a speculative fiction writer and playwright, a retired archirect with a master of architecture degree in theory, and a theater producer, director, and acting improvisor. I'm currently working on a TV series of 169 episodes exploring life in a contemporary parallel universe very much like...

I know that there exists non-geometrical proofs that the usual mapping of the Klein Bottle in ##\mathbb{R}^3## is an immersion. But I would like to see an actual geometrical 'test'. I was thinking if saying that on the self intersection, which I circled in red below, the map being injective can...

Recently, in my quantum physics classes i was introduced to the concept of tunneling of particle through a barrier potential and about transmission probability. Our instructor mentioned about something known as "Klein tunneling". Can somebody explain to me what is Klein tunneling and why...

Hi everyone, I've been reading about the Klein Gordon equation with the Coulomb Potential. The full solution can be found here: http://wiki.physics.fsu.edu/wiki/index.php/Klein-Gordon_equation#Klein-Gordon_equation_with_Coulomb_potential I'm confused near the beginning of this. I understand...

So I'm trying to understand how the Torus is a 2-sheet covering of the Klein bottle. I found this on math exchange: https://math.stackexchange.com/questions/1073425/two-sheeted-covering-of-the-klein-bottle-by-the-torus. The top response add's rigor to of the OP's observation that the double...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] I think I understand part b) . The idea is to move the operator that annihilates to the RHS via the commutator relation. However I can't seem to get part a. I have: ## [ P^u, P^v]= \int \int \frac{1}{(2\pi)^6} d^3k d^3 k'...

Hello! I am reading about Klein Gordon operator from Peskin book and he reaches at a point the integral ##\int_0^\infty \frac{1}{p^2-m^2}e^{-ip(x-y)}dp^0##. He then explains the different approaches of doing this integral, depending on how you pick the contour around the 2 poles. Why does the...

Hello, I tried looking this up a lot and just could not find it. For four bar linkage, Klein's construction is used to find velocity and acceleration of piston and connecting rod. Here is a link for the procedure of the same...

From time to time, I point to string theoretists that they should have considered more seriously to use Kaluza-Klein theory and they invariably answer me "we do", and move forward. So I am starting to thing that perhaps I am wrong and I have missed some developing of the theory the the XXIth...

Hello! I read that the Klein-Gordon field can be viewed as an operator that in position space, when acted upon vacuum at position x creates a particle at position x: ##\phi(x) |0 \rangle \propto |x \rangle##. It make sense intuitively and the mathematical derivation is fine too, but I was...

This is a follow on from the following thread where I put a little 'challenge' to the OP. https://www.physicsforums.com/threads/when-can-klein-gordon-equation-be-used-for-photon.906767/ It probably didn't really interest him so he didn't do it, but I thought I would post it anyway - its quite...

Hello! I am trying to work out the various cases for the potential step problem in the context of the Klein Gordon equation. I was wondering if one must consider the situation where E<mc^2 when working out the situation of E-mc^2 <V< E+mc^2 where V is the value of the potential after the step...

How a klein bottle has a 0 volume? I am a 12th grade student and i don't know anything about topology,klein bottles but i am curious to know how something which exist has a 0 volume. I just watched clifford stoll's klein bottles video on numberphile and i came here to know how a klein bottle has...

If space-time is curved like a klein bottle, is it theoretically possible that events could loop back in time ? :wink:

If equation of motion(K-G Eqn.,) follows, ∂μ∂μΦ+m2Φ=ρ where 'ρ' is point source at origin. How time independent form of above will become, (∇2-m2)Φ(x)=gδ3(x) where g is the coupling constant, δ3(x) is three dimensional dirac delta function.

micromass submitted a new PF Insights post Groups and Geometry Continue reading the Original PF Insights Post.

Hey folks, I'm not certain if this is the right board to put this in(I couldn't figure where else itd go). I've been thinking about the Klein bottle and had a curious thought. Since the 'bottle' is a 4d object with only one face, it can be navigated in its entirity via two dimensions. You can...

The quantum Klein-Gordon field ##\phi({\bf{x}})## and its momentum density ##\pi({\bf{x}})## are given in Fourier space by ##\phi({\bf{x}}) = \int \frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2 \omega_{{\bf{p}}}}} \big( a_{{\bf{p}}} e^{i{\bf{p}} \cdot {\bf{x}}} + a^{\dagger}_{{\bf{p}}}...

QUOTE: "In 1929, physicist Oskar Klein[1] obtained a surprising result by applying the Dirac equation to the familiar problem of electron scattering from a potential barrier. In nonrelativistic quantum mechanics, electron tunneling into a barrier is observed, with exponential damping. However...

I've done some reading on quantum field theory, and I went over how when Schrodinger first derived this equation, he discarded because it yielded negative energy solutions, negative probability distributions and it gave an incorrect spectrum for the hydrogen atom. The book then went on to state...

Homework Statement a)Show that the yukawa potential is a valid static-field euation b)Show this solution also works Homework EquationsThe Attempt at a Solution Part (a) Using the relation given, I got LHS = \frac{e^{-\mu r}}{r} \left[ (m^2 - \mu^2) - \frac{2\mu}{r} - \frac{2}{r^2}...

http://en.wikipedia.org/wiki/Kaluza–Klein_theory ##http://link.springer.com/article/10.1007/BF01390677 (original german paper, Ich kan nicht Deutsche) http://www.scientificexploration.org/journal/jse_21_3_beichler.pdf (this author makes some interesting arguments) Also, a lot (if not all...

Hello! I'm studying various dark energy models, and as a part of the project, I need to be able to numerically solve the Klein-Gordon (KG) equation and the Friedmann Equation (FE) in the context of a canonical scalar field. I wasn't sure whether or not this belonged here or in the computational...

I was reading about the Klein Gordon equation of scalar fields. I notice that the hamiltonian is not Hermitian: ∂0(Φ,π)T = matrix((0,1),(-p2,0)) (Φ,π)T The Hamiltonian operator iH = matrix((0,1),(-p2,0)) is not a hermitian matrix. What does this mean? Does this mean Klein Gordon fields don't...

Can someone please read the attached file and tell me his ideas? I want to be sure I understand the action of the Klein Four group...Is my interpretation correct? I have some problem though. The Klein Four group has 4 elements, and it is able to describe the reflective symmetries of a square...

I would like to interest the PF community in a collective activity based on some topics we have discussed from time to time. We know that there are seven dimensional manifolds whose isometry group is the same that the standard model gauge group. But they are not enough to get the standard...

Hi everyone! Im' a new member and I'm studying Quantum Field Theory. I read this: "The interpretation of the real scalar field is that it creates a particle (boson) with momentum p at the point x." and : \phi\left(x\right) \left|0\right\rangle = \int \frac{d^3p}{(2\pi)^3(2\varpi_p)}...

I am reading James Munkres' book, Elements of Algebraic Topology. Theorem 6.3 on page 37 concerns the homology groups of the Klein Bottle. Theorem 6.3 demonstrates that the homology groups for the Klein Bottle are as follows: H_1 (S) = \mathbb{Z} \oplus \mathbb{Z}/2 and H_2 (S) = 0 I...

Is there any experiment about Kaluza-Klein Theory ? If there is some experiments, What are the results of them ?

Hi all! I was reading up on the Klein paradox in Itzykson & Zuber's Quantum Field Theory (but I think this is a pretty standard part that's probably present in most QFT textbooks) and on page 62 they have a pretty straight forward solution to the Dirac equation with a step potential. I've...

In this note (http://sgovindarajan.wdfiles.com/local--files/serc2009/greenfunction.pdf) the Klein-Gordon retarded green function is derived on the form $$G_{ret}(x − x′) = \theta(t − t') \int \frac{d^3 \vec k}{(2\pi)^3 \omega_k} \sin \omega_k (t − t′) e^{i \vec{k}\cdot (\vec x - \vec x')}$$...