All Questions
74
questions
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93
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The Klein-Gordon Propagator According to Peskin and Schroeder (Derivation of *Retarded* Green's Function)
On page 29 of Peskin and Schroeder's An Introduction to Quantum Field Theory, the authors write that the propagator is given by:
$$\begin{align}
\langle 0|[\phi(x),\phi(y)]|0\rangle&=\int{d^3p\...
- 4,399
1
vote
0
answers
67
views
Derivation of massive photon propagator
I'm trying to derive the massive photon propagator using the path integral formalism for a theory with
$$
\mathcal{L} = -\dfrac{1}{4} F_{\mu\nu} F^{\mu\nu} + \dfrac{1}{2} m^2 A_\mu A^\nu, \text{with } ...
- 1,611
0
votes
1
answer
95
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Exponential decay of propagator outside lightcone
In Tong's lecture notes (http://www.damtp.cam.ac.uk/user/tong/qft.html) page 38, he calculates the following propagator:
$$D(x-y) = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_\vec{p}} e^{-ip \cdot (x-y)}....
- 665
2
votes
2
answers
148
views
Derivation of propagator for Proca action in QFT book by A.Zee
Without considering gauge invariance, A.Zee derives Green function of electromagnetic field in his famous book, Quantum Field Theory in Nutshell. In chapter I.5, the Proca action would be,
$$S(A) = \...
- 529
0
votes
0
answers
71
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Integral Representation of Modified Bessel Function in Position-Space Feynman Propagator
I am working through a problem on deriving the explicit form of the position-space Feynman propagator. I have found, with thanks to many posts on this site, 2-3 different ways of performing the ...
- 19
0
votes
0
answers
254
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Explicit Form of Feynman Propagator for a Scalar Field in Position-space: Derivation Details
This is Problem (6.1) from Schwartz's QFT and the Standard Model. I am trying to directly calculate, by performing the integral over momenta, the explicit position-space expression of the Feynman ...
- 19
1
vote
0
answers
79
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Proving that Retarded K-G Propagator is Green function (Peskin & Schroeder 2.56) [closed]
I am trying to derive Peskin & Schroeders expression $2.56$:
$$(\partial^2 +m^2)D_R(x-y)=-i\delta^{(4)}(x-y)\tag{2.56}$$
with $$D_R(x-y)=\theta(x^0-y^0)\langle 0|[\phi(x),\phi(y)]|0\rangle.\tag{2....
- 538
1
vote
1
answer
69
views
Feynman propagator from Hadamard propagator
The Feynman propagator is defined as
$$i G_F = \theta(t-t')G^+ + \theta(t'-t)G^-. \tag{1}$$
Using
$$G^{(1)} = G^+ + G^-,$$
$$G_R = -\theta(t-t')G, $$
$$G_A = \theta(t'-t)G, $$
$$\bar{G} = \frac{1}{2}(...
0
votes
1
answer
59
views
Finding scalar propagators in QFT for specific spacetime dimension $d$ and mass $m$
I need to understand how in practice one finds propagators for given $d$ and $m$ in quantum field theory. I can write down the theory provided for it but I don't know how to use it.
We will compute ...
- 1
3
votes
1
answer
460
views
Propagator for a massless scalar field in $d$-dimensional spacetime [closed]
I'm trying to show that for a free massless scalar field, the 2-point correlation function in $d$-dimensional spacetime has the following form:
$$<\phi(x)\phi(y)> = \int \frac{d^d{p}}{(2\pi)^d}\...
2
votes
0
answers
121
views
How to use Ward identity to abbreviate the photon propagator into $\frac{-i\ g_{\mu\nu}}{q^2 (1- \Pi(q^2))}$?
How to derive abbreviated form (equation 7.75) from original form (equation 7.74) via Ward identity? (In Peskin's QFT Charpter 7 P246)
I still can't see this result after read this paragraph many ...
1
vote
3
answers
414
views
Yukawa decay at one-loop
I am trying to calculate the amplitude for a decay $\phi \to e^+e^-$ under a Yukawa interaction $\mathcal{L}_I = -g\phi \bar{\psi}\psi$ to one-loop order (with massless fermions for simplicity).
If I'...
- 23
1
vote
0
answers
44
views
Feynman parametrization with three denominators [duplicate]
I'm triyng compute some integral loops for my thesis and I need use Feynman's parametrization with three denominators, I've used the general formula like:
\begin{equation}
\frac{1}{A_1A_2...A_n}=(n-1)!...
0
votes
1
answer
86
views
Operator inversion to get propagator [closed]
The propagator $\Delta(p)$ satisfies the relation:
$$\left(p_\mu p_\nu -p^2 g_{\mu\nu}+\frac{n_\mu n_\nu}{\xi}\right)\Delta^{\nu\rho} = i\delta^\nu_\rho.$$
Thus $\Delta(p)$ is obtained by inverting $\...
1
vote
0
answers
444
views
One-loop correction $\phi^4$ theory
Consider the following one-loop diagram:
The corresponding expression in momentum space is:
\begin{equation}
(-i\lambda)\int \dfrac{i}{k^2-m^2+i\epsilon}\frac{d^4k}{(2\pi)^{2}}
\end{equation}
(...
- 146