All Questions
17
questions
1
vote
1
answer
181
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Calculate first-order term of the $S$-matrix for the $\phi^{4}$ theory [closed]
Before I ask a question, I will start with a small introduction.
I want to evaluate the $S$-matrix order-by-order in an expansion in small $\lambda$ for a $2 \rightarrow 2$ scattering in $\phi^{4}$ ...
- 237
1
vote
0
answers
47
views
How to apply multiple Klein-Gordon operators to products of propagators?
I have the 4-point correlation function for a scalar free field
$$
\langle{0} | T \phi_1 \phi_2 \phi_3 \phi_4 | 0 \rangle = -\left[ \Delta_F(x_1-x_2) \Delta_F(x_3-x_4) + \Delta_F(x_1-x_3) \Delta_F(x_2-...
- 601
0
votes
1
answer
50
views
Why are all the possible permutationss in the perturbative $S$-matrix calculations added together?
I have a question regarding the calculation of the $S$-matrix. During the calculation of second order term of the $S$-matrix for e.g. the Møller scattering $(e^
− + e^
− → e^
− + e^
−)$ $|i\rangle=|e^...
- 172
1
vote
0
answers
206
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Calculating a four-point Green function using Wick's theorem (problem 12.1 in Mandl & Shaw)
In problem 12.1 in Quantum Field Theory, Mandl & Shaw the aim is to calculate the four point green function
$$ G^{\mu\nu}(x,y,z,w) = \frac{\langle 0 | T\big(A^{\mu}A^{\nu}\psi(z)\bar{\psi}(w)S\big)...
- 311
1
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1
answer
133
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Computing $\langle 0|S |0\rangle$ in $\phi^4$ theory [closed]
$\newcommand{\bra}[1]{\langle #1|}$
$\newcommand{\ket}[1]{|#1\rangle}$
I have been reading David Tong's QFT notes. As part of an exercise, I am asked to examine $\bra{0} S \ket{0}$ to order $\lambda^2$...
- 111
3
votes
1
answer
708
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Scalar derivative couplings: Effects on S-matrix and Feynman Rules
In Schwartz's field theory book ch. 7.4.2 he claims that interaction Lagrangians like
$${\cal L}_{\rm int} = \lambda \phi_1(\partial_{\mu}\phi_2)(\partial_{\mu}\phi_3)\tag{7.101}$$
lead to the Feynman ...
- 447
4
votes
1
answer
614
views
Feynman propagator for interacting field
For scalar field, Feynman propagator is commonly defined as
$$
\Delta_F(x-y) = \langle 0 | T\phi(x)\phi(y)|0 \rangle .
$$
For free theory, field satisfy equation of motion is $$\phi(x) = \int\frac{dp^...
- 337
1
vote
1
answer
1k
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Meaning of a strange Feynman diagram for the $\phi^3$ scalar Field theory
Background
I am considering a scalar field theory with $\sim\phi^3$ interaction term, with Lagrangian
\begin{equation}
\mathcal{L} = \frac{1}{2}\left( \partial_\mu\phi\right)^2 - \frac{m^2}{2}\phi^2 - ...
- 107
0
votes
1
answer
196
views
Particle Creation by a Source
I am currently self-studying Quantum Field Theory and am using the textbook Introduction to Quantum Field Theory by Peskin and Schroeder. Currently I am in chapter 4, and am doing the first problem in ...
user261609
5
votes
1
answer
692
views
On contractions and S-Matrix in $\phi^4$ scalar theory
If you have a self-interacting Lagrangian for a scalar field theory:
$$L= L_0 + L_I = \frac{1}{2} (\partial_\mu\phi)^2 - \frac{1}{2} m^2\phi^2- \frac{g}{4!}\phi^4$$
where $g$ is the coupling constant, ...
- 373
2
votes
1
answer
374
views
On which propagator does the field self-contraction loop go on this Feynman diagram?
This question relates to page 111 in Peskin and Schroeder.
I am trying to do the derivation of the 2-particle to 2-particle Feynman diagrams in $\phi^4$ theory by hand, following Peskin and Schroeder. ...
- 6,963
2
votes
1
answer
1k
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$\phi^4$-theory, S-matrix Feynman diagram to first order from Peskin and Schroeder
This relates to page 111 in Peskin and Schroeder.
We have the $\phi^4$ S-matrix for a 2-particle to 2-particle scattering reaction:
$$-i\frac{\lambda}{4!}\int d^4x \langle p_1p_2|\mathcal T\left(\phi(...
- 6,963
1
vote
0
answers
129
views
What exactly are we doing when we "invent" Feynman Diagrams?
So, I am trying to derive the Feynman rules for Yukawa theory (following the section in Peskin). Specifically, for the process 2 fermions $\rightarrow$ 2 fermions. To second order, I then have that ...
- 4,780
1
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1
answer
673
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How to use Wick's theorem to compute this matrix element?
I wanted to see how to use Wick's theorem in practice (I know with Feynman diagrams it is better, but here I want to do this with Wick's theorem only), so I considered computing the matrix element for ...
- 36.4k
1
vote
0
answers
122
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Wick contraction in proton-pion production
Proton-pion production $\gamma + p \rightarrow \pi^0 + p$ occurs through the interaction hamiltonian $$\mathcal H_{int} = ig \bar \psi^{(p)} \gamma_5 \psi^{(p)} \phi + e \bar \psi^{(p)} \gamma_{\mu} \...
- 3,569