What is Propagator: Definition and 200 Discussions

In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the respective diagram. These may also be viewed as the inverse of the wave operator appropriate to the particle, and are, therefore, often called (causal) Green's functions (called "causal" to distinguish it from the elliptic Laplacian Green's function).

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  1. J

    Propagator and delta functions

    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'...
  2. M

    Srednicki's Lehmann-Kallen propagator derivation doubt

    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...
  3. Hepth

    Feynman Rules : Propagator Question

    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...
  4. S

    Zee QFT In a Nutshell Propagator Question

    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...
  5. N

    Understanding the Propagator in Quantum Field Theory

    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...
  6. S

    Geostationary orbit propagator

    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 *...
  7. B

    Propagator for a free particle / schrodinger equation

    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,->...
  8. L

    Loop corrections to the propagator

    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...
  9. D

    Feynman propagator on the cylinder - position space representation

    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...
  10. I

    Difference between s-matrix and interactive field propagator?

    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...
  11. R

    Is the locality of the propagator affected by the value of M?

    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...
  12. C

    Compute SHO Propagator: Eigenfunction Expansion

    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...
  13. H

    Maxwell propagator in Kaku's QFT book

    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...
  14. Q

    Rewriting the propagator for the free particle as integral over E

    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}...
  15. W

    Causality and the Role of Propagator in Quantum Field Theory

    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...
  16. S

    Non relativistic limit for dirac propagator

    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...
  17. maverick280857

    Path Integral Propagator Normalization in Lewis Ryder's QFT book

    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...
  18. maverick280857

    Question about the Klein Gordon Propagator

    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...
  19. N

    When is a propagator on shell?

    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...
  20. N

    Why Photon Momentum Drops Out of QED Propagator

    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...
  21. G

    Branch-cut singularity and the multiparticle contribution to the full propagator

    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...
  22. R

    Probability distribution function / propagator

    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...
  23. R

    Solving Mark Srednicki QFT: Exact Propagator Problems (13.12, 13.13, 13.16)

    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...
  24. S

    Questioning the Propagator: Diagonal or Not?

    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...
  25. C

    Massive vector (Proca) propagator

    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...
  26. I

    Non-covariant parts of the propagator?

    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...
  27. P

    What is the Correct Form of the Free Propagator in QFT?

    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 )...
  28. S

    Feynman propagator as distribution

    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...
  29. tiny-tim

    Propagator - Hankel function - infinite? - Weinberg

    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...
  30. W

    Understanding the Klein-Gordon Propagator and its Satisfying Equation

    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)...
  31. B

    Massive boson propagator - problem with step in derivation

    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}...
  32. J

    Finding Graviton Propagator from QFT in a Nutshell- Zee's Exercise

    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...
  33. L

    Gluon propagator in the infrared

    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...
  34. W

    How Do You Solve for the Propagator in Momentum Space Under Constant Force?

    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 }...
  35. S

    Typo in Kapusta or Ashok Das ? Formula for thermal propagator

    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...
  36. Hans de Vries

    Deriving the Dirac propagator 'purely' from causality

    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...
  37. M

    What is the graviton propagator in the first order formalism?

    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...
  38. E

    What Happens When Propagator Formalism Is Applied to an Eigenstate?

    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...
  39. E

    Propagator Equation at t=0 Explained

    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...
  40. E

    Why adj( U(t)) * U(t) = I where U(t) is a propagator in QM?

    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.
  41. E

    Propagator Equation: Explaining Integral

    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?
  42. P

    Propagator for a particle in free space

    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...
  43. J

    What is Propagator in Quantum Mechanics?

    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(...
  44. K

    Can the semiclassical propagator be defined using a Hamilton-Jacobi equation?

    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...
  45. H

    Definition of the dressed propagator

    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...
  46. F

    Propagator counterterm in phi^4

    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...
  47. S

    Second-Order Graviton Propagator in Rovelli-Smolin's Loop Quantum Gravity

    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...
  48. E

    Why Does Inserting a Mass Width Simulate Higher Order Diagram Effects?

    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...
  49. K

    Photon propagator in an arbitrary gauge

    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...
  50. E

    What is the Green inverse function for a given propagator?

    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?
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