Klein-gordon Definition and 87 Threads

There exists Green's Functions such that the solutions appear to be retro-causal. The Klein-Gordon equation allows for antiparticles to propagate backwards in time. Does this mean the future can influence the past and present? Then again The Poincare Recurrence Theorem states that over a...

Does anyone know how to write the classical solution to the Klein-Gordon equation in NON natural units? Where do all the c's and h's go?

It is said that the solutions of the Klein-Gordon equation cannot be interpreted as probability densities since the norm isn't conserved in the time evolution. Now a pretty evident idea seems to be to renormalize the solution at each moment so that it is renormalized (and hence interpretable...

So I'm trying to find a solution of the Klein-Gordon equation for a massless particle. I reached the Klein-Gordon from the total energy-momentum equation. Then for a massless particle i get to this equation: $${ \partial^2 \psi \over \partial t^2 } = c^2 \nabla^2 \psi$$How do I solve for psi? I...

Hi! I read a text were some kind of "Schroedinger-equation" for a neutrino field is being derived. But there is a particular step I do not understand. Consider a Dirac field \psi(t, \vec{x}) of a neutrino, satisfying the Klein-Gordon equation: \left( \partial_{t}^{2} + \vec{k}^{2} +...

Hello, I have a question. In Ryder chapter 2, he develops the KG equation and says something along the lines of "the density, in order to be relativistic, must transform like the time component of a 4 vector" and he immediately gives: \rho=\frac{i\hbar}{2m}\left(\phi^*\frac{\partial...

Usually in the first sentence of the definition of the Klein Gordon equation is the statement that it describes spin-0 particles. Similarly, in the first sentence of the definition of the Dirac equation is the statement that it describes spin-1/2 particles. But then comes the bit that got...

Please teach me this: We know that 0-spin particles obey Klein-Gordon equation and 1/2spin particles obey Dirac equation.But I do not know whether higher integer spin particles obey Klein-Gordon equation or not.Similarly,do higher half integer spin particles obey Dirac equation?Because if we...

I am reading through 'An Introduction to QFT' by Peskin & Schroeder and I am struggling to follow one of the computations. I follow writing the field \phi in Fourier space ϕ(x,t)=∫(d^3 p)/(2π)^3 e^(ip∙x)ϕ(p,t) And the writing the operators \phi(x) and pi(x) as ϕ(x)=∫(d^3 p)/(2π)^3...

I was reading the book written by Peskin about QFT when I found that the following equation: (\frac{\partial}{\partial t^2}}+p^2+m^2)\phi(\vector{p},t)=0 has as solutions the solutions of an Harmonic Oscillator. From what I know about harmonic oscillators, the equation describing them should...

[/tex]1. Homework Statement [/b] Given: \phi(x)=\phi^+(x)+\phi^-(x) Where: \phi^+(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a(\mathbf{k}) \mathrm{e}^{-\mathrm{i}kx} and \phi^-(x)=\sum_{\mathbf{k}} \sqrt{\frac{\hbar c^2}{2 V \omega_{\mathbf{k}}}} a^\dagger...

Hi all. I'm taking my first foray into QFT, and have a question which is hopefully pretty basic. I think I understand the concept itself, I just don't quite get how the math works out. I'm right at the beginning, in the discussion of how to set up the creation/annihilation operators for a...

massless Klein-Gordon equation not conformally invariant?? Wald discusses conformal transformations in appendix D. He shows that the source-free Maxwell's equations in four dimensions are conformally invariant, and this makes sense to me, since with photons all you can do is measure the...

since the time derivative is second order, the KG equation can not be put in the form i \dot{\psi}= H \psi so there is no H in KG equation? and no Heisenberg picture for KG equation?

Homework Statement Hi everyone, in Peskin & Schroeder, P36, the derivative part of KG field is transformed as eqn (3.3). But why does the partial derivative itself not transform? Homework Equations \partial_{\mu} \phi (x) \rightarrow \partial_{\mu} ( \phi ( \Lambda^{-1} x) ) = (...

Hi, I've had the following problem in elementary quantum field theory. The propagator for the Klein-Gordon scalar field takes the form D(x-y)=\int\frac{\textrm{d}^3\mathbf{p}}{(2\pi)^3}\frac{1}{2\sqrt{|\mathbf{p}|^2+m^2}}e^{-ip\cdot(x-y)} I was interested what the propagator looks like for...

Hi. I'm following the solution of a Klein-Gordon PDE in a textbook. The equation is \begin{align} k_{xx}(x,y) - k_{yy}(x,y) &= \lambda k(x,y) \\ k(x,0) &= 0 \\ k(x,x) &= - \frac{\lambda}{2} x \end{align} The book uses a change of variables $\xi = x+y$, $\eta = x-y$ to write \begin{align}...

Hey guys, Was wondering if anyone has seen this done? Essentially I've tried plugging in the Schwarzschild exterior metric and getting a radial wave equation then taking a series expansion for small M (gravitating mass) and comparing that to the KG radial wave equation in a radial potential...

Hi Following a request by FunkyDwarf (I don't know if dwarfs have odor!) in https://www.physicsforums.com/showpost.php?p=2556673&postcount=11" thread, regarding how one can get the Klein-Gordon equation (KGE) for free particles in a gravitational field, i.e. the equation -g^{\mu \nu}...

The Lagrangian is given by, \sum_{a=1}^N \left[(\partial^{\mu}\phi_{a}^{\ast})(\partial_{\mu}\phi_{a})-m^{2}\phi_{a}^{\ast}\phi_{a}\right]. Is the symmetry SO(2N), SU(N) or U(N)? It seemed quite obvious to me and some of my friends that such theory has an SO(2N) symmetry. If we view...

The conserved current for a field \phi obeying the Klein-Gordon equation is (neglecting operator ordering) proportional to i\phi^{\dag}\partial_\mu \phi-i\phi\partial_\mu \phi^{\dag}. The conserved current for a four component field \psi obeying the Dirac equation is...

Homework Statement Given the Lagrangian density of a complex relativistic scalar field \mathcal L=\frac{1}{2}\partial^\nu\phi^{*}\partial_\nu\phi-\frac{1}{2}m^2\phi^{*}\phi where * stands for complex conjugation, compute the conserved current (using Noether's theorem). Homework Equations I...

Homework Statement Sort of stuck deriving the Klein-Gordon equation from Heisenberg equation of motion \dot{\varphi} = i [H, \varphi ] Homework Equations \dot{\varphi} = \frac{\partial\varphi}{\partial t} H = \int d^3x \mathcal{H} \Pi (x) = \dot{\varphi}(x) \mathcal{H} = \Pi...

Homework Statement I'm trying to derive the Klein-Gordon equation from its lagrangian density \mathcal{L} = - \frac{1}{2} \partial^{\mu} \varphi \partial_{\mu} \varphi - \frac{1}{2} m^2 \varphi^2 + \Omega_0 (Srednicki p.24) Homework Equations S = \int d^4x \mathcal{L}...

I have an exact solution to the Klein-Gordon equation with linear potential. But I am only an amateur physics enthusiast with no incentive (or time) to do anything with it, nor familiarity enough with the physics to know if it is interesting and, if so, interesting to whom. It has been sitting...

Does the Klein-Gordon Lagrange density maximize or minimise the solution of the Klein-Gordon equation?

Currently I am working through a script concerning QFT. To introduce the concept of canonical filed quantisation one starts with the (complex valued) Klein-Gordon field. I think the conept of quantising fields is clear to me but I am not sure if one can claim that the equations of motion for the...

Why are my formulas not displayed correctly?

Dear all, I'd be very grateful for some help on this question: "The momentum operator is defined by: \displaystyle P = - \int_{0}^{L} dz \left(\frac{\partial \phi}{\partial t}\right) \left( \frac{\partial \phi}{\partial z} \right) Show that P can be written in terms of the operators a_n...

I'd be greatful for a bit of help on this question, can't seem to get the answer to pop out: A particle moving in a potential V is described by the Klein-Gordon equation: \left[-(E-V)^2 -\nabla^2 + m^2 \right] \psi = 0 Consider the limit where the potential is weak and the energy is...

[SOLVED] Evaluate the Klein-Gordon action I'm interested in evaluating the Klein-Gordon action in P&S, p. 287. It goes as follows S_0 = \frac{1}{2} \int d^4 x \! \phi \left( - \partial^2 -m^2 \right) \phi + \left(\text{surface term} \right) The surface terms drops out, that's fine. I...

Can we imagine electro-magnetic field in vakuum as a massless particle that respects Klein-Gordon equation (instead of Electromagnetic wave equation)? It seems to me that both equations are the same, except that the electro-magnetic field can have 2 possible polarizations (then we count them...

Homework Statement Homework Equations Show that the KG propagator G_F (x) = \int \frac{d^4p}{(2\pi)^4} e^{-ip.x} \frac{1}{p^2-m^2+i\epsilon} satsify (\square + m^2) G_F (x) = -\delta(x) The Attempt at a Solution I get (\square + m^2) G_F (x) = - \int \frac{d^4p}{(2\pi)^4} (p^2-m^2)...

[SOLVED] Klein-Gordon Causality calculation Homework Statement In Peskin and Schroeder on page 27 it is stated that when we compute the Klien-Gordon propagator in terms of creation and annihilation operators the only term that survived the expansion is...

I'm just reading the schroeder/peskin introduction to quantum field theory. On Page 21 there is the equation \phi(x)=\int\frac{d^3 p}{(2\pi)^3}\frac{1}{ \sqrt{2\omega_{\vec{p}}} } (a_{\vec{p}} e^{i \vec{p} \cdot \vec{x}} +a^{+}_{\vec{p}} e^{-i \vec{p} \cdot \vec{x}} ) and in the...

Is it correct to think, that with a scalar complex Klein-Gordon field the wave function \Psi:\mathbb{R}^3\to\mathbb{C} of one particle QM is replaced with an analogous wave functional \Psi:\mathbb{C}^{\mathbb{R}^3}\to\mathbb{C}? Most of the introduction to the QFT don't explain anything like...

Homework Statement I do not understand how the Klein-Gordin equation can hold when you have a del operator on one side and a partiall derivative on the other. Doesn't the del operator give a vector and the partial derivative operator yield a scalar? Homework Equations The...