Propagator Definition and 180 Threads

This is more of a math question than a physics one, but following the discussion of the propagator in Zee's book: -(∂2+m2)D(x-y)=δ(x-y) he then gets, by taking the Fourier transform of the Dirac delta and dividing through: D(x-y) = \int\frac{d^4k}{2π^4} \frac{e^{ik(x-y)}}{k^2-m^2+iε}...

Hi all, I've been playing around with (2.54) of Peskin and Schroeder, and I've some quick questions about it. Firstly, the part I'm stuck on: $$\int\frac{d^3p}{(2\pi)^3}\left[\left.\frac{1}{2E_p}e^{-ip\cdot (x - y)}\right|_{p^0=E_p} - \left.\frac{1}{-2E_p}e^{-ip\cdot (x -...

Hello. I was trying to find out the propagator for the inverted SHO (something like tachyon oscilltor) and turns out that it remains unitary only for very short times. Which didnt make much sense to me. I tried looking at the usual SHO propagator, and that too seems to be not Unitary! ( I...

Hi! From "Le Bellac, Quantum and statistical field theory, 10.5.2-Massive vector field": "The longitudinal part of the propagator k_{\mu}D^{\mu\nu} has no pole at k^2=m^2, so the longitudinal part doesn't constitute a dynamical degree of freedom." I have two questions: 1) Why the propagator...

So I am wondering about one thing. The charged propagators in weak theory are W+- bosons. The mathematical expression for them, while drawing the Feynman diagrams is: -i\frac{g_{\mu\nu}-\frac{q_\mu q_\nu}{m_W^2}}{q^2-m_w^2}. The problems that are usually given to me are simple and involve...

Hi all, I'm trying to figure out the link between the connection coefficients (Christoffel symbols), the propagator, and the coordinate description of the covariant derivative with the connection coefficients. As in...

Hi all, I've been fiddling around with this problem for a while. I intuitively understand that the parallel propagator is the path integral of the connection. I would like to be able to show the converse (connection is derivative of parallel propagator) mathematically, and I am having a...

Dear PF, I am a little bit confused could you pls help me ... Suppose I a have a scatering or conversion of two particles via graviton propagator. Graviton propagator couples with energy-momentum tensor of matter fields. So can i assume that vertex to which graviton propagator is coupled...

So in the attachment, in fact (6), the formula for the propagator rectangled in red... is the Hamiltonian ACTING on (t-t')? is the Hamiltonian a function of (t-t')? or should it be (this is what I think), to be more clear U(t,t') = exp((-i/h)(t-t')H), so that when acting on a state...

Well I am doing an assignment concerning methods of finding Feynman's propagator. I understand pretty well how everything's coming up. I also get that the form: <x'',t'|x',0> defined as Feynman's propagator gives the amplitude of a system initially being in state |x',0> to be in |x'',t> after...

The Dirac propagator (e.g. for an electron) is given by the inverse of the field equation in momentum space i.e. (\displaystyle{\not} p - m)\psi = 0, which gives: \frac{i}{(\displaystyle{\not} p - m)} = \frac{i(\displaystyle{\not} p + m)}{(p^2-m^2)}. So is the propagator for a Majorana...

Could anyone please explain the sequence below taken from Mandl QFT textbook (p.53)? 1. i\hbar c\Delta^+(x-x')=[\phi^+(x),\phi^-(x')] 2. i\hbar c\Delta^+(x-x')=\langle 0|[\phi^+(x),\phi^-(x')]|0\rangle 3. i\hbar c\Delta^+(x-x')=\langle 0|\phi^+(x)\phi^-(x')|0\rangle 4. i\hbar...

Hi, If I have a matrix valued field B(x)_i^{..j}=B^a (x) (T^a)_i^{..j} and the relevant part of my Lagrangian is L=Tr(-\tfrac{1}{2}\partial^{\mu}B\partial_{\mu}B+..) then how can I see that the propagator for the matrix field is...

So, Shankar in his famous book started to use the propagator a bunch of times in his Simple Problems in One Dimension chapter, and I have been confused to what it is and does.

Hi. I am stuck. By inverting the spin-1 differential operator I was able to derive (quite easily) the propagator for the spin-1 field (in a spontaneously broken gauge theory) in the R_\xi gauges for the arbitrary gauge parameter \xi. The result is...

Hi everyone! Something has been bothering me lately. Consider the quark propagator: \langle 0|\psi_a(x)\psi_a(0) |0\rangle For a given color a. Now let's say we insert 1 = \sum |n \rangle \langle n| between the two quark fields, where the sum is over a complete set of energy...

Hi, I'm working with the free space linearized gravitation lagrangian and trying to derive the proper propagator for it. I have no problem doing this, the only problem is that my QFT makes a quick note of what form this should take and I'm off by a factor of 4. The flatspace metric terms...

Hi! I have a process with multiple feynman diagrams where gluon propagators occur. When I use an axial gauge for the gluon propagator, do I have to use the same n-vector for every propagator? Following this I wonder whether I can use the same n-vector for every polarization sum in axial gauge...

On page 68, equation (8.13) of Srednicki's QFT book is the equation for the scalar propagator: \Delta(x-x')=i\theta(t-t') \int \frac{d^3k}{2(2\pi)^3E_k}e^{ik(x-x')} +i\theta(t'-t) \int \frac{d^3k}{2(2\pi)^3E_k}e^{-ik(x-x')} where the exponential is the product of 4-vectors and k is...

The integral: \int \Pi_k d\phi_k e^{-\phi_i A_{ij} \phi_j} is a Gaussian and is equal to: (\pi)^{n/2}\sqrt{det(A^{-1})}= (\pi)^{n/2} e^{\frac{1}{2}Tr ln A^{-1}} Now usually A is a diagonal matrix that represents the Lagrangian (so that the sum over i and j collapses to a sum just over i...

If one wants, to calculate the self energy correction to the electron propagator(using the approach where one introduces a photon mass \mu to deal with IR divergences), one gets after some work an integral like this (this is from the Itzykson Zuber book equ. 7-34): \int_ 0 ^ 1 d\beta \beta...

I'm reading Zee's QFT textbook and I'm stuck trying to understand why the \delta^\mu_\lambda appears when he defines the propagator of a massive spin-1 boson as the inverse of a differential operator: [(\partial^2 + m^2)g^{\mu\nu}-\partial^\mu\partial^\nu]D_{\nu\lambda} = \delta_\lambda^\mu...

Homework Statement Attempting a problem related to a quantum particle in free fall due to constant force (old exam question) \begin{align*}H = \frac{1}{{2m}} P^2 + m g X\end{align*} The last part of the question asks to verify that the position space propagator has the following form...

Homework Statement Show that G(q_2,q_1;t)=\mathcal{N}\frac{e^{iS_{lc}}}{\sqrt{\det A}} where \mathcal{N} is a normalization factor independent of q1, q2, t, and w. Using the known case of w=0, write a formula for G such that there is no unknown normalization factor. Homework Equations I...

Integration in Sean Carroll's "parallel propagator" derivation Reading Chapter 3 of Sean Carroll's General Relativity Lecture Notes, I've followed it up to and including eq. 3.38. \frac{d}{d\lambda} P^\mu_{\;\;\; \rho}(\lambda,\lambda_0) = A^\mu_{\;\;\; \sigma} P^\sigma_{\;\;\...

Hi, I have a question about the relation between the propagator of a scalar field and the heat kernel. I'm not sure wether I should rather put this question into the math section: Given a Laplacian D on some manifold M, what I mean by heat kernel is just K(x,y;s) = \langle x | \exp(-sD)...

hi I don't understand this bit about the derivation of propagator expressions. Bjorken and Drell describe the step function as: \theta(\tau)=lim_{\epsilon \to 0}\frac{-1}{2\pi i}\oint_{-\infty}^{\infty}\frac{d\omega e^{-i\omega r}}{\omega + i \epsilon } the singularity is at -i \omega...

I'm probably missing something small but I haven't been able to figure this out. In the Feynman rules (for a scalar field that obeys the Klein-Gordon equation), you write a propagator for internal lines as \frac{i}{k^2 - m^2 + i \epsilon}. The propagator integrand is originally...

I'm trying to show that the propagator for spacelike separation decays like e^{-m r} and I'm stuck. At some point I hit the integral \int_{-\infty}^{\infty} \frac{dk}{\sqrt{k^2 + m^2}} e^{i k r}. Integration of complex functions not being my forte, I only managed to get to this point...

The propagator D for a particle is basically the Green's function of the differential operator that describes that particle, e.g. (\partial^2 + m^2) D(x-y) = \delta^4 (x-y). This propagator is supposed to give the probability of the particle propagating from x to y. Why does this make...

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...

This may be more of a maths question, but because I may actually just be interpreting the expression wrong, I think I'd better post it here. I'm reading Quantum Field Theory in a Nutshell by A. Zee and I'm stuck on a bit of maths he does. He provides an expression for the free propagator for a...

In Kaku's book, the self-energy in a \phi^4 scalar theory is expanded in a Taylor series as: \Sigma(p^2)=\Sigma (m^2)+\Sigma'(m^2)(p^2-m^2)+\tilde_{\Sigma}(p^2) where \tilde_{\Sigma}(p^2) is finite and m is arbitrary (but finite). The full propagator is then...

http://en.wikipedia.org/wiki/Propagator What does this equation mean: \Big(H_x - i\hbar\partial_t\Big) K(x,t,x',t') = -i\hbar\delta(x-x')\delta(t-t') Wouldn't it be more relevant to emphasize these equations: \Big(H_x - i\hbar\partial_t\Big) K(x,t,x',t') = 0,\quad\quad t\neq t'...

Homework Statement Problem with the ordering of integrals in the derivation of the Lehmann-Kaller form of the exact propagator in Srednicki's book. We start with the definition of the exact propagator in terms of the 2-point correlation function and introduce the complete set of momentum...

I know I should know this, but I have a quick question. Let's say we have a diagram: 1-->----------2 | | <- "q" v | 3--<----------4 Lets assume: 1 = "quark" 3 = "antiquark" 2 = W boson 4 = photon q = same quark flavor as "3" Time...

I've started working through Zee's book and have got to question I.3.2 - calculation of D(x) in 1+1 dimensions for t=0. The expression to evaluate becomes (omitting constant multipliers for simplicity) \int^{\infty}_{-\infty} dk \frac{e^{ikx}}{\sqrt{k^2+m^2}} This is singular at k=+im...

Hello PF :) Let me for the moment consider just <0|\varphi(y)\varphi(x)|0> as a propagator (instead of commutator of the fields)... and so in this expression evolves only <0|aa^{+}|0> part. Now my question is: 1) We can consider this expression as <0|a vector multiplied by a^{+}|0> which...

Hi guys, I've been trying to make a longitude and drift rate propagator for a geostationary satellite but the equations do not take into account other perturbing forces apart from the Earth's triaxiality. Longitude = Initial Longitude + Initial Drift Rate * Elapsed Time + 0.5 *...

http://img18.imageshack.us/img18/4295/eqn.png here is the text preceding the exercise: http://yfrog.com/5mch5p in the exercise, where does the factor \frac{m}{(2mE)^{1/2}} come from? Comparing that equation with 5.19 (bottom right of link), why can't we just replace |p> with |E,+> and |E,->...

Hi, I have a couple of questions on this (mostly based on Srednicki ch14). If I understand things correctly the difference between the exact propagator (always shown in bold in Srednicki) and the "usual propagator" from earlier chapter (i.e. the one corresponding to lines in the Feynman graphs...

Hi all! Does anyone know the position space representation of the Feynman propagator on the cylinder? The momentum space representation is the same as in Minkowski 2D space, but the position space representation is different because the integrals over momenta are now sums. Or could someone...

In an interactive field theory we can compute the amplitude of a particle propagating from y to x by evaluating perturbatively expressions of the form <GS|o(x)o(y)|GS> where GS stands for ground state and o are the field operators. This can be extended to higher number of operators for more...

What does it mean to say that the propagator G(x,x')=\int \frac{d^4p}{(2\pi)^4}\left(\frac{e^{ip(x-x')}}{p^2+M^2}\right) is nonlocal? Does that mean that if x and x' are space-like in separation, this expression is non-zero? If you did have something local represented by a Fourier...

I know how to do SHO propagator by computing the action. I was only trying to do it via the eigenfunction expansion K(x’,x;t)=sum_ i phi_i(x’) phi_i(x) exp(-iε_it/hbar )=(m omega/pi*hbar) sum_i=-^infty h_i(y’) h_i(y) exp[-(y**2+y’**2)/2] [s(t)/2]**i with s(t)=exp(-iomega t) This...

In Michio Kaku's QFT book, p. 106, he writes: [To illustrate problems with direct quantization due to gauge invariance] let us write down the action [of the Maxwell theory] in the following form: \mathcal L=\frac12 A^\mu P_{\mu\nu}\partial^2A^\nu where...

Homework Statement (This is all with respect to a free particle) Show that the propagator U(t) = \int_{-\infty}^{\infty} |p><p| exp\left(\frac{-i E(p) t}{\hbar}\right) dp can be rewritten as an integral over E and sum over the \pm index as: U(t) = \sum_{\alpha = \pm}...

Hi All, I am currently reading stuff about the propagator and causality in QFT at the moment and I don't really understand it. Could anyone explain this to me? I understand that a propagator is a function which describes how particles and anti-particles travel from one place to another, but...

Hi everybody, I don't know if this is the right section to ask for such a question but I have been dealing with this problem for a while and there's something I still cannot grasp... Let us suppose that we have a dirac free particle with propagator (i'm sorry but I'm not able to obtain the...

Hi, In Lewis Ryder's QFT book on page 160, the propagator for the case when the Lagrangian can be written as L = \frac{p^2}{2m} + V(q) is given as \langle q_f t_f|q_i t_i \rangle = \lim_{n\rightarrow\infty}\left(\frac{m}{i\hbar\tau}\right)^{(n+1)/2}\int...