All Questions
28
questions
1
vote
1
answer
181
views
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
2
votes
1
answer
198
views
Symmetry Factor and Wicks Theorem
I have a problem with a particular kind of exercise. The question is:
Consider $\phi^4$-theory with $\mathcal{L}_\text{int}=-\frac{\lambda}{4!}\phi^4$. Give the symmetry factors of the diagram and ...
- 23
0
votes
1
answer
90
views
Greiner´s Field Quantization question [closed]
I upload a screenshot of Greiner´s book on QFT. I don´t understand one step. I need help understanding equation (3), what are the mathematical steps in between?
Greiner, Field Quantization, page 245 (...
- 15
0
votes
1
answer
352
views
Two-point correlation function of two complex scalar fields
For a lagrangian:
$$
\mathcal{L}=\partial^\mu\phi_i^*\partial_\mu\phi_i-m_i^2|\phi_i|^2+\lambda(\phi_2^3\phi_1+\text{h.c.}).
$$
where summation over $i=1,2$ is understood.
I am trying to find the two ...
- 129
1
vote
1
answer
357
views
Wick Theorem: number of contractions [closed]
I have to prove that the number of contractions in Wick's Theorem
is equal to:
$$\frac{n!}{(n/2)! \ 2^{n/2}} \ \ \ where \ \ n \ \ is \ even$$
I don't know how to start, if someone can help.
1
vote
0
answers
144
views
Scalar Yukawa theory, contraction
In the scalar Yukawa theory ($\Phi$ is real scalar field and $\phi$ is a complex scalar field):
\begin{equation}
\mathcal{L}_{S Y}=\left(|\partial \phi|^{2}-m^{2}|\phi|^{2}\right)+\frac{1}{2}\left((\...
- 357
2
votes
1
answer
559
views
Help with Wick's theorem in a $\phi^4$ QFT
QFT noob here. I am currently working out the momentum space two-point function for a $\phi^4$ qft in Euclidean space time, and considering the $\lambda^1$ order contribution, I am encountering a ...
- 675
3
votes
1
answer
305
views
How do I show that the $n$-point correlator $\left\langle\phi(x_1)\phi(x_2)...\phi(x_n)\right\rangle$ is equal to this expression?
Given the Euclidean action \begin{equation}
S_E(\phi) = \int d^d x \frac{1}{2}\big(\nabla\phi\cdot\nabla\phi + m^2\phi^2\big)\end{equation} and the partition function \begin{equation}\mathcal{Z} = \...
0
votes
0
answers
158
views
How to find all possible Wick contractions of 5 fields?
I need to find all possible contractions (in the sense of Wick contractions) for 5 fields. One can of course start drawing randomly, but I'm sure there is some kind of algorithm to do this ...
3
votes
1
answer
112
views
Number of Wick contractions for $\left< x ( t^\prime )^5 x ( t^{\prime \prime} )^5 \right>$
I am considering the possible Wick contractions for the following expression:
\begin{align*}
\left< x ( t' )^5 x ( t'' )^5 \right> = \left< x( t' ) x( t' ) x( t' ) x( t' ) x( t' ) x( t'') x(...
- 3,856
1
vote
0
answers
85
views
How to calculate the invariant amplitude for a decay process using wick's theorem?
I have difficulties to apply Wick's theorem to the following problem-set:
We have three free scalar fields $\phi_1, \phi_2, \phi_3$. While the field $\phi_3$ has the mass $M$ while $\phi_1$ and $\...
- 11
1
vote
1
answer
322
views
Wick theorem exercise [closed]
I'm a newbie in QFT and I have some doubts with this simple exercise:
Using the Wick Theorem evaluate
$$\langle0|T(\phi^4(x)\phi^4(y)|0\rangle$$
Use a diagrammatic approach to represent the possible ...
- 37
1
vote
1
answer
408
views
How to obtain time-ordered density correlation function of free Bosonic system via Wick's theorem?
Consider a free Bosonic system. The Hamiltonian is given by
$$
H=\sum_k \frac{k^2}{2m}a_k^\dagger a_k.
$$
Since the spectrum is gapless, the ground state can be of any particle number (or even ...
- 118
1
vote
1
answer
159
views
Perturbation expansion with path integrals
This is from Hugh Osborn's 'Advanced Quantum Field Theory' notes, Lent 2013, page 15.
I want to evaluate the expression
$$ Z = \exp\Big(\frac{1}{2} \frac{\partial}{\partial \underline{x}} . A^{-1} \...
- 1,075
2
votes
0
answers
158
views
OPE Kac-Moody Currents
We have the following operators:
\begin{align}
J^a(z) = \frac{1}{2}\psi_s^{\dagger}(z)\sigma^a_{s s'}\psi_{s'}(z), \hspace{10 mm} \bar{J}^a(z) = \frac{1}{2}\psi_s^{\dagger}(\bar{z})\sigma^a_{s s'}\...
- 41