Propagator Definition and 200 Threads

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...

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...

Hey all, just a simple question that's confusing me about amplitudes for feynman diagrams. How do i know whether a system needs to be considered as being on shell, and hence has an imaginary component included in the denominator of the propagator? If i have one propagator which is required...

Since the 4-vector A couples to the conserved current j^\mu = \psi-bar gamma^\mu \psi in QED, k_\mu Fourier-transform(j^\mu) = 0. The Fourier-transform of j is a mess. Is there an easy way to see why terms containing photon momentum k_\mu drop out of the photon propagator in practical QED...

I have been reading Chapter 7 of Peskin & Schroeder about full propagator, the Kallen Lehman spectral representation, and got stuck at the branch cut singularities and at the complex logarithm of negative numbers. I have posted in the Analysis forum (but have not received any answer) the...

I have the following equation: \frac{1}{2N^{2}}\int_{s} \int_{p} \left\langle (\textbf{R}_{s} - \textbf{R}_{p} )^{2} \right\rangle which describes the radius of gyration of a polymer. (the term being integrated is the average position between beads p and s) This is shown to be...

I've got a question about about eqns. 13.12, 13.13, and 13.16. in Mark Srednicki's QFT book, freely previewable here: http://www.physics.ucsb.edu/~mark/qft.html (it's a good book - this is the only section I have problems with) I don't really get how he derives the Lehmann-Kallen form...

This might turn out to be a stupid question but ...i couldn't understand The propagater is defined as exp[-iHt/(h/2pi)]...this would be the matrix so U(t)|\psi(x,0)> (matrix . vector) would give |\psi(x,t)> What i couldn't understand is that the propagator is a diagonal matrix..but it is...

Hi all, I'm stuck with this following problem: Homework Statement Consider the Proca action, S[A_\mu] = \int \, \mathrm d^4x \left[ - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 m^2 A_\mu A^\mu \right] where F_{\mu\nu} = 2 \partial_{[\mu} A_{\nu]} is the anti-symmetric electromagnetic...

I'm reading Weinberg's volume I. I don't quite understand what's the origin of the non-covariant parts of the propagator. The propagator can be calculated to be \Delta_{\ell m}(2\pi)^{-4}\int d^4q\frac{P_{\ell m}(q)\,e^{iq\cdot(x-y)}}{q^2+m^2-i\epsilon}\quad\cdots(*) where P_{\ell...

Homework Statement from Zee QFT in a nutshell the free propagator between two "sources" on the field is given by D(x_\mu) = -i \int \frac{d^3k}{(2\pi)^3 2 \omega_k}[e^{-i(\omega_kt-k\bullet x)} \Theta(x_0) + e^{i(\omega_k t-k\bullet x)} \Theta(-x_0) for a space like separation ( x_0 = 0 )...

Hi, This question is quite relevant to some other posts at the end of the very long "very simple QFT questions" thread, but I've decided to start a new thread with a heading which is more indicative of what I wish to ask the group. As a question, it's a fairly concise, but the analysis is...

I'm completely confused by page 202 of Weinberg's QTF, Vol.I. In particular: I can't find "Hankel" anywhere on PF, and wikipedia is no real help. Surely integral (5.2.8) doesn't converge (the integrand oscillates between ±1)? In fact, I think it's -∞. :redface: So how can it be a...

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)...

I've been going through a derivation of the massive boson propagator. The only trouble is I don't feel satisfied by one particular step. I've started getting the problem written up in tex so here goes: \newcommand{\del}{\partial}...

On page 36 of QFT in a nutshell, Zee sets an exercise to find the propagator for a massive spin 2 particle by assuming that it is a linear combination of terms such as G_{\mu\nu}G_{\lambda\sigma}. The only method I can think up for doing this is to write down all 36 products of...

I have read some recent preprints in arxiv recently: http://arxiv.org/abs/0709.2042 http://arxiv.org/abs/0704.3260 http://arxiv.org/abs/hep-th/0610148 about the behavior of the gluon propagator in the infrared. Recent lattice computations seem to support them (e.g...

Homework Statement (this is from R. Shankar, Principles of Quantum Mechanics, 2nd ed, exercise 5.4.3) Consider a particle subject to a constant force f in one dimension. Solve for the propagator in momentum space and get U(p,t;p',0) = \delta (p-p'-ft) e^{ i(p'^3-p^3)/6m\hbar f }...

typo in "Kapusta" or "Ashok Das"? Formula for thermal propagator Hi! Does somebody of you have Kapusta's book "finite temperature field theory" and Ashok Das book (same title)? I'm quite sure there is a typo in one of them - compare the formulas for the Fourier transformed thermal propagator...

I figured out this one, just thought it was quite nice... We start with the only requirement that the Green's function of the propagator is causal in the sense that it propagates stricktly forward in time, so that the Green's function is zero at t<0. Using the Heaviside step function we can...

With the help of harmonic gauge condition, graviton propagator can be obtained by weak field expansion around the flat Minkowski metric (assuming cosmological constant is zero). Gravitation theory can also be written in the first order (Palatini) formalism. In stead of the metric, the basic...

If you use propagator formalixm to calculate the future time dependence of a state that starts in an eigenstate, what happens? The equation for the propagator is K(x, x';t,0) = \sum_n \psi_n^*(x')\psi_n(x)e^{-iE_nt/\hbar So if we start in an eigenstate does that mean that the...

I understand the progator in general but could someone explain this equation for the propagator at t = 0 for me: \delta(x' - x) = K(x',x;0,0) = \sum_m \psi_n(x')\psi_n(x) ? I am confused about the dfiference between x' and x. It seems like the Kronecker would make more sense than Dirac...

This is probably really obvious but can someone explain to me why adjiont( U(t)) * U(t) = I where U(t) is a propagator in QM and I is the identity.

Can someone explain to me why the equation \psi(x,t) = \int{U(x,t,x',t')\psi(x',t')dx'} where U is the propagator has an integral? I thought you could just multiply the propogator by an initial state and get a final state?

Sorry for not following the template but as I'm not answering a problem it didn't seem apropriate. Hopefully this is the right place to put this (it seems somewhere between introductory and advanced). Just when I thought I was getting my head round this stuff I'm completely stuck on how the...

Here's how I've learned propagators, and how far I felt I understood them. For a shrodinger's equation i\hbar\partial_t\Psi = -\frac{\hbar^2}{2m}\nabla^2 \Psi the propagator is K(t,\boldsymbol{x},\boldsymbol{y}) =\int\frac{d^3p}{(2\pi\hbar)^3}\exp\Big(-\frac{i}{\hbar}\Big(...

If we have SE (or other differential equation) defining the propagator by: (\frac{\partial}{\partial t}-H(q,p))G(x,s)=\delta (x-s) then my question is..can you define a "semiclassical" operator?..i mean in the sense that it would solve approximately the equation (1) above but in WKB...

In section 7.3 of Ryder's "Quantum Field Theory", the "complete" or "dressed" propagator is defined to be the two-point function to all orders of the perturbation expansion. It is denoted in (7.71) as G_c^{(2)}(x, y). It changes the bare mass to the physical mass. My question is, why aren't...

Hello--I'm looking at Peskin p.324-323 where he describes the renormalization of \phi^4 theory. I'm a little confused about the Feynman rules that one gets out of the lagrangian with counter terms. My question in a nutshell: The propagator is given by \frac{i}{p^2 - m^2}, why is it that the...

I have finished a quick first reading of the rovelli at all paper ingraviton propagator http://arxiv.org/gr-qc/0604044 I couldn´t dive too much into the details because spin foams was a prerequisite and i only could do an equally fast reading of the alejandro perez review of the subjecto...

When calulating near resonant cross sections one usually inserts a mass width in the denominator of the propagator. This should, at least as I have understood it, correspond to taking the higher order diagrams into account. What I would like to see is a proof for the equivalence between...

My aim is to derive the photon propagator in an arbitrary gauge. I follow Itzykson-Zuber Quantum Field Theory and start from the Lagrangian with gauge-fixing term: {\cal L}(x) = -\,\frac{1}{4}\,F_{\mu\nu}(x)F^{\mu\nu}(x) - \,\frac{1}{2\xi}\,(\partial_{\mu}A^{\mu}(x))^2 I get the following...

given the propagator: G(x,t)=\frac{1}{e^{xt}+1} and knowing that HG(x,t)=d(x-t) with d the "delta" function and H the Hamiltonian,then how could we construct (knowng G(x,t))the Hamiltonian?... I one work i heard about the Green inverse function, how is it calculated?