What is Feynman propagator: Definition and 16 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. M

    The propagator of eigenstates of the Total Angular Momentum

    To show that when ##[J^2, H]=0 ## the propagator vanishes unless ##j_1 = j_2## , I did (##\hbar =1##) $$ K(j_1, m_1, j_2 m_2; t) = [jm, e^{-iHt}]= e^{iHt} (e^{iHt} jm e^{-iHt}) - e^{-iHt} jm $$ $$ = e^{iHt}[jm_H - jm] $$ So we have $$ \langle j_1 m_1 | [jm, e^{-iHt} ] | j_2 m_2 \rangle $$ $$ =...
  2. Glenn Rowe

    A Feynman propagator for a simple harmonic oscillator

    I'm reading through Lancaster & Blundell's Quantum Field Theory for the Gifted Amateur and have got to Chapter 17 on calculating propagataors. In their equation 17.23 they derive the expression for the free Feynman propagator for a scalar field to be...
  3. binbagsss

    Did I Misinterpret the Change of Sign in the Feynman Propagator Integral?

    Homework Statement [/B] Hi in the first attachment I am stuck on the sign change argument used to get from line 2 to 3 , see below Homework Equationsabove The Attempt at a Solution [/B] Q1) please correct me if I'm wrong but : ##d^3 p \neq d\vec{p} ## since ##d^3 p = dp_x dp_y dp_z ## and...
  4. Q

    A What is the "real" Feynman propagator?

    The logic of the Feynman Propagator is confusing to me. Written in integral form as it is below $$\Delta _ { F } ( x - y ) = \int \frac { d ^ { 4 } p } { ( 2 \pi ) ^ { 4 } } \frac { i } { p ^ { 2 } - m ^ { 2 } } e ^ { - i p \cdot ( x - y ) },$$ there are poles on the real axis. I have seen...
  5. J

    Flux-flux correlation function under Feynman's path integral

    This is a chemically inspired problem, but the path is fully quantum mechanics and a bunch of integrals. How does one calculate fully quantum mechanical rate ($\kappa$) in the golden-rule approximation for two linear potential energy surfaces? Attempt: Miller (83) proposes...
  6. binbagsss

    I QFT Feynman Propagator Algebra

    I am wanting to get the expression up to ##O(\epsilon^{2}) ## : To show that ##\frac{1}{2w_{k}} (\frac{1}{w_{k}-k_{0}-i\epsilon} + \frac{1}{w_{k}+k_{0}-i\epsilon})## ##=## ## \frac{1}{k_{v}k^{v} + m^{2} - i\epsilon}##, [2] where ##w_{k}^{2}=k^{2}+m^{2}##, ##k## the variable, and (this seemed...
  7. S

    Evaluation of Feynman propagator in position space

    Homework Statement Compute ##\displaystyle{\int\ \frac{d^{4}p}{(2\pi)^{4}}} \frac{i}{p^{2}-m^{2}+i\epsilon}e^{-ip \cdot{(x-y)}}## in terms of the invariant interval. Interpret your answer in the limit of small and large invariant intervals and for zero mass. Homework Equations The Attempt...
  8. G

    Huygens principle in odd/even dimensional flat space

    A well known math theorem says that - if the spatial dimension is odd - D'Alembert equation gives rise to a solution containing a term which is completely supported on the light cone. A mathematical wrap up could be the following: "in dimension 3 (and in fact, for all odd dimensions), the...
  9. Quantioner

    The Wick rotation in position space

    The Feynman propagator is $$ G_{F}(x) = \int d^4p \, \frac{e^{-ip x}}{p^2 - m^2 + i\epsilon}. $$ I want to understand why the directions of Wick rotation in position space and momentum space are contrary. Every book I find says something like "we should keep ##xp## unchanged", but why? As we...
  10. N

    Evaluating Time-Ordered Product with Wick's Theorem

    Homework Statement [/B] Consider a real free scalar field Φ with mass m. Evaluate the following time-ordered product of field operators using Wick's theorem: ∫d^4x <0| T(Φ(x1)Φ(x2)Φ(x3)Φ(x4)(Φ(x))^4) |0> (T denotes time ordering) Homework Equations Wick's theorem: T((Φ(x1)...Φ(xn)) = ...
  11. T

    Advanced/retarded Feynman propagator?

    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...
  12. Xenosum

    Intuitive Description of Feynman Propagator?

    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...
  13. Greg Bernhardt

    How Does the Feynman Propagator Define Particle Movement in Quantum Mechanics?

    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, the...
  14. J

    Feynman propagator and particle uniqueness

    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...
  15. 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...
  16. 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...
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