Propagator Definition and 180 Threads

I'm reading the ## \frac 1 N ## chapter of Sidney Coleman's "Aspects of Symmetry". Equation 3.5, gives the gluon propagator as below: ## A^a_{\mu b}(x)A^c_{\nu d}(y)=\left( \delta^a_d \delta^c_b-\frac 1 N \delta^a_b \delta^c_d \right) D_{\mu \nu}(x-y)##. Then he explains that the term...

I'm reading these lecture notes but there is something I don't understand. In page 15, it starts to consider vacuum diagrams of various orders and tries to associated a factor to them according to the rule: ## diagram \sim (\frac \lambda N)^p(\frac N \lambda)^v N^l=\lambda^{p-v} N^{l+v-p}##...

Homework Statement The integral I want to solve is $$ D(x) = \frac{-i}{8\pi^2}\int dr\,d\theta \frac{e^{-irx\cos\theta}}{\sqrt{r^2+m^2}}r^2\sin\theta$$ which I've reduced to $$ D(x) = \frac{-i}{4\pi x}\int dr \frac{r\sin(rx)}{\sqrt{r^2+m^2}} $$ by integrating over ##\theta##. However, I...

Homework Statement I'm working through Zee for some self study and I'm trying to do all the problems, which is understandably challenging. Problem 1.3.1 is where I'm currently stuck: Verify that D(x) decays exponentially for spacelike separation. Homework Equations The propagator in question...

Why isn't (5.298) the following instead? ##K(x, t_1; x', t_0) = \delta(x-x')\,e^{-\frac{i}{\hbar}H(t_1-t_0)}## My reasoning: Since \Psi(x, t_1) = e^{-\frac{i}{\hbar}H(t_1-t_0)}\,\Psi(x, t_0)\\ = e^{-\frac{i}{\hbar}H(t_1-t_0)}\,\int\delta(x-x')\Psi(x', t_0)\,dx' The exponential operator with...

Hi i want to find propagator of inverse harmonic oscillator to find time dependent wave function, but I can't have any ideas about this. Is it possible to help me to find it Thanks

Can someone help with what must be a simple math issue that I'm stuck on. Shankar ("Principles of Quantum Mechanics" p. 153) evaluates the propagator for a free particle in Equation 5.1.10. A scan of the chapter is available here...

I am hung up on what must be a very elementary matter, but I’m unable to see where I’m wrong. I reference R. Shankar's "Principles of Quantum Mechanics". For the free particle with https://www.physicsforums.com/file:///C:/Users/DANIEL~1.ABR/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png ...

Its usually said that the propagator ## K(\mathbf x'',t;\mathbf x',t_0) ## that appears as an integral kernel in integrals in the path integral formulation of QM, is actually the Green's function for the Schrodinger equation and satisfies the equation below: ## \left[ -\frac{\hbar^2}{2m}...

Homework Statement Consider the following scalar theory formulated in two-dimensional Euclidean space-time; S=∫d2x ½(∂μφ∂μφ + m2φ2) , a) Determine the equations of motion for the field φ. b) Compute the propagator; G(x,y) = ∫d2k/(2π)2 eik(x-y)G(k). Homework Equations Euler-Lagrange equations...

Homework Statement I have the following massive spin-1 propagator- $$ D^{\mu\nu}(k)=\frac{\eta^{\mu\nu}-\frac{k^{\mu}k^{\nu}}{m^2}}{k^2 - m^2} $$ I want to write down the propagator in the imaginary time formalism commonly used in thermal field theories. Homework EquationsThe Attempt at a...

How does the wavefunction propagate for infinitesimal times? Please no Feynman path integral arguments!

Hello! On p.145 of Shankar's Principles of Quantum Mechanics, the author derives the general propagator for the Schrodinger equation in the following manner. Shankar's working Expanding the state vector in the energy basis, |\psi(t)\rangle = \sum_{E} |E\rangle \langle E| \psi(t) \rangle...

In A. Zee "QFT in a nutshell" in chapter I.5 Exercise 1.5.1 on page 39 for spin 2 massive propagator. I know I’m missing something very simple (self-taught beginner). I'm trying to derive equation (13) on page 35, which is G_{\mu\nu,\lambda\sigma} = G_{\mu\lambda}G_{\nu\sigma} +...

Ｉ Want to analyze the decay from a excited nucleon to a nucleon and an Omega meson.I have seen a propagator which descripes a process : a→b+c (Eur. Phys. J. A16, 537–547 (2003), Covariant tensor formalism for partial-wave analyses ofψdecay to mesons ,B.S. Zou and...

Hi there, As in Ta-Pei Cheng and Li's book for example the W boson propagator is given by : ## \frac{-i}{k^2-M^2} [g_{\mu\nu}+ (\zeta-1) k_\mu k_\nu/(k^2 - \zeta M^2)] ## At the unitary gauge ## \zeta = \infty ##, where the W propagator becomes : ## \frac{-i}{k^2-M^2} [g_{\mu\nu}- k_\mu...

I have a question that is very basic and could not seem to find it online or I have not searched the right way. What is the propagator of a scalar boson? I found that of a fermion line and that of a vector boson but could not find that of a scalar boson.

I want to find a simple example of using the Feynman propagator: 1/(|x-x'|2-(t-t')2) and also to show that no signals an travel faster than light. So I was thinking about waves emitted from an antenna. Tell me if I got this right? Assume a static source in space at x=0 and varying in time...

For internal photon states, is it necessary to sum over the longitudinal polarization state in addition to the transverse states? And if so, does the ordinary Feynman-gauge propagator take care of this? Thanks!

Within the path integral framework, the reason you have to use Fadeev-Popov quantization for spin 1 is because the matrix of the coefficients of the quadratic part of the free-Lagrangian is non-invertible. But doesn't an i\epsilon prescription take care of that? The same thing happens with the...

is there a discussion somewhere on the notion of an advanced or retarded feynman propagator. i don't mean the advanced or retarded propagator juxtaposed against the feynman propagator. I mean the feynman propagator itself with a theta step function multiplied by it to effectively give an...

Hello everybody. I have a free scalar in two dimensions. I know that its propagator will diverge for lightlike separations, that is t= ±x. I have to find the prefactor for this delta function, and I don't know how to do this. How do I see from, for example, \int \frac{dk}{\sqrt{k^2+m^2}} e^{i k...

Homework Statement The Feynman Propagator is given by <0| T \phi(y)\phi(x) |0> , where T is the time-ordering operator. I understand that this turns out to be the solution to the inhomogeneous klein-gordon equation, etc., but is there any intuitive description of the propagator? Can this...

Hi people! Today I was doing some QFT homework and in one of them they ask me to calculate the Harmonic Oscillator propagator, which, as you may know is: W(q_2,t_2 ; q_1,t_1) = \sqrt{\frac{m\omega}{2\pi i \hbar \sin \omega (t_2-t_1)}} \times \exp \left(\frac{im\omega}{2\hbar \sin \omega...

Does anybody know a good reference for the gluon propagator at two loop? I need it in Feynman gauge, but to have it in light-cone gauge as well is a plus. Preferably a paper, or a book that is common (i.e. easy to find in our university's library :-) ). Thanks!

Well I'm trying to understand the difference between these propagators: \frac{g_{\mu \nu}}{k^{2} - m^2 + i \epsilon} and \frac{g_{\mu \nu}+ \frac{ k_{\mu} k_{\nu}}{m^{2}}}{k^{2} - m^2 + i \epsilon} My professor told me that they are different gauges, and the from the second you rule out...

I am confused about the very step from Eq.(14) to Eq.(15) in the paper http://arxiv.org/pdf/hep-ph/0308157.pdf There is one ##ig## in (14), while ##(ig)^2## in (15), where does it come from? Regards!

I would like to ask when can someone add the width in a scalar particle's propagator. In general the scalar propagator can be: \frac{1}{k^{2}-m^{2}+i \epsilon} (\epsilon \rightarrow 0) However I read somewhere that if necessary one can include a width for the propagator...

[SIZE="4"]Definition/Summary The Feynman propagator \Delta_F(x) is the propagator (the probability amplitude) for a scalar particle of non-zero mass, m, to travel over a space-time interval x. It is obtained by integrating, over all possible 3-momentums \mathbf{q} of a particle of mass m...

Considering the real-time quantum propagator originated by the green's function of the time-dependent Schrödinger equation: i\hbar \frac{d\psi}{dt} =H\psi namely, \psi(t) =e^{-i\hbar H t}\psi(0) it is straightforward to see that using as basis set the eigenvector of H\phi_k...

Hi everyone. I was trying to reproduce the calculation needed to include the QCD correction to the low energy electroweak Lagrangian. In particular I am looking at Peskin section 18.2. In equation 18.35 an extra minus sign appears on the numerator of the second fermion propagator. Can anyone...

In page 30 of book "An introduction to quantum field theory" by Peskin and Schroeder in the derivation of Klein-Gordon propagator, why p^0=-E_p in the second step in equation (2.54). and why change "ip(x-y)" to "-ip(x-y)"? I thought a lot time, but get no idea. Thank you for your giving me an...

Hello, I've been given a problem which is asking me to flesh out a calculation. The calculation is word for word like this; So I am being asked to work this out in detail, fill in all the steps. I thought that maybe I should try and show that the four momentum squared is not conserved at...

The propagator in 4-dimensions for a free scalar field has the form: Δ(x,0)=Θ(t)A(x,t)+Θ(-t)B(x,t) where Θ is the step function (eq 23 of Zee's QFT book, 2nd edition). He then makes the claim that for spacelike x, one can set t=0, and define Θ(0)=1/2. The going through all the math, he...

In his layman's guide to QED Feynman defines a particle propagator as a function that gives you the amplitude that a particle, that was initially at spacetime event ##x##, will be found at spacetime event ##y##. But does this definition assume that the particle is unique so that if you find...

Hi! I have encountered a little problem. I want to show that the explicit form of the Feynman propagator for massless scalar fields is given by: \begin{align} G_F(x) & = - \lim_{\epsilon \to +0} \int \dfrac{\mathrm{d}^{4}k}{(2 \pi)^{4}} \dfrac{1}{k^{2} + i \epsilon} \mathrm{e}^{- i k...

Good afternoon fellow scientists,i have a small problem in evaluating the propagator for the complex Klein-Gordon field. Although the procedure is the one followed for the computation of the propagator of the real K-G field, a problem comes up: As known: <0|T\varphi^{+}(x)\varphi(y)|0> =...

Hello all, In Carroll's there is a brief mention of how to get an idea about the curvature tensor using two infinitesimal vectors. Exercise 7 in Chapter 3 asks to compute the components of Riemann tensor by using the series expression for the parallel propagator. Can anyone please provide a...

Hello all, I have a fundamental problem with the concept of the propagator regarding to time dependent potential. If the propagator is based on the expansion of the time evolution operator, how can it act on initial wave function in the presence of time dependent potential? You cannot use the...

Homework Statement Show that [\hat{\phi}(x_1),\hat{\phi}^\dagger(x_2)] = 0 for (x_1 - x_2)^2 < 0 where \phi is a complex scalar field Homework Equations \hat{\phi}=\int\frac{d^3 \mathbf{k}}{(2\pi)^3 \sqrt{2\omega}}[\hat{a}(k)e^{-ik\cdot x} + b^\dagger(k)e^{ik\cdot x}]...

Hello, I'm looking at the following computation from the Peskin and Schroeder's book: See file attached In the second page, the second term that's being integrated, I don't understand why it has a negative i in the exponential, that'll keep the energy term the same, but will swap the sign...

The propagator $$\frac{1}{k^2+m^2} $$ diverges in the ultraviolet when integrated over all dkn, with n>=2. However, when you throw in an exponential, $$\Delta(x)=\int d^nk \frac{e^{ikx}}{k^2+m^2} $$ is convergent for x≠0 Intuitively adding the oscillating exponential decreases the...

The result of the Kallen-Lehmann spectral representation is that the two point correlation (and thus also the full propagator) has a pole in the physical mass of the particle. In Peskin and Schroeder it is also argued that multiparticle states show up as a cut, but bound states can also show up...

One can show that at around ##p \approx m## where m is the physical mass the full propagator ##D_F## is something like $$D_F = \frac{Z}{p^2 - m^2}.$$ Where ##Z = (1 - \Sigma '(m))^{-1}##, ##\Sigma## is the self energy and m is the physical mass of the particle. If i were now to write a...

Hi, I am trying to write down the propagator for a scalar field theory, but I want to try and get it in the functional representation. My plan is to compute the following: \langle \psi (x', t') | \psi (x,t) \rangle which gives the amplitude to go from x' to x. Now I guess I have to...

Hi all, I am studying QFT using John Preskill's notes. I have a question about the propagator and poles. On page 2.91, at the bottom, he said that there is a s-channel pole, which is the pole of the exact propagator. Then he claimed that by the argument about unitarity in page 2.70, the pole...

Hey again, I have a question on a couple of things related to feynman diagrams but also the relativistic scalar propagator term. First of all, this interaction: The cross represents a self-interaction via the mass and characterised by the term: -im^2, is this just some initial state...

Hi, It's great to find this forum. I'm teaching myself QM using Shankar, it's a great book, I've covered 8 chapters so far. My question is about the notion of using Path Integral method to calculate the propagator. The recipe given by Shankar says the propagator is U(x,t;x')=A\int...

Why must it be true that a system that has a bound state must have its scattering amplitude have a pole in the upper half of the complex wave-number plane? For example, if the scattering amplitude as a function of the initial wave number magnitude |k| is: A=\frac{1}{|k|-iB} with B>0, then...

Hey Everyone, I've a quick a question regarding the make-up of bosonic Green's functions, taking the free propagator for phonons as example. According to Mahan, 3rd ed. it is given by: D(q, \lambda, t-t')=-i\langle0|TA_{q}(t)A_{-q}(t')|0\rangle with A_{q}=a_{q}+a^{+}_{q} [ Eqs...