Propagator Definition and 180 Threads

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'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}...

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...

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?