All Questions
86
questions
2
votes
1
answer
93
views
Equivalent definitions of Wick ordering
Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
- 3,350
2
votes
1
answer
130
views
Non-perturbative matrix element calculation
Following Peskin & Schroeder's Sec.7's notation, I would like to compute the matrix element
$$
\left<\lambda_\vec{p}| \phi(x)^2 |\Omega\right>\tag{1}
$$
where $\langle\lambda_{\vec{p}}|$ is ...
- 78
2
votes
1
answer
161
views
Confusion regarding simplifying normal ordered products in CFT
I am studying CFT on my own and have some confusion regarding applications of Wick's Theorem to simplify normal ordered products to time ordered products. Wick's theorem is fairly straightforward, ...
- 904
3
votes
2
answers
281
views
Wick contraction between two scalar fields
I have a short question about Wick contraction.
It is given that $$\phi\left(x\right) = \phi^{+}\left(x\right) + \phi^{-}\left(x\right)\tag{1}$$ where:
$$\phi^{+}\left(x\right) = \int \frac{d^3p}{\...
- 237
1
vote
0
answers
74
views
Doubt regarding use of Wick contractions
I'm currently taking my first course in QFT and am learning about finding transition amplitudes using Wick's theorem. As far as I'm aware, Wick's theorem gives us a way to change from a time-ordered ...
- 139
2
votes
1
answer
154
views
Doubt on scattering amplitude in scalar Yukawa theory
I'm currently following David Tong's notes on QFT. In the section on calculating transition amplitudes using Wick's theorem, he gives an example using a scalar Yukawa theory with real scalar field $\...
- 139
0
votes
0
answers
40
views
Vacuum expecation value of normal ordered product, Peskin/Schroeder
I'm working through Peskin/Schroeder where they treat time ordered product of fields in the interactin picture. The Wick Theorem was introduced as
$$T\{\phi(x_1)\dots\phi(x_n)\}=N\{\phi(x_1)\dots\phi(...
- 315
0
votes
2
answers
85
views
The vanishing of vacuum expectation value
I have some difficulty understanding why the vacuum expectation value vanishes. As illustrated in my notes, we can split the field into two parts:
$$
\phi(x) = \phi^+(x) + \phi^-(x),
$$
where $\phi^+(...
- 41
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
1
vote
0
answers
110
views
Defining Wick/normal ordering beyond rearranging the order of annihilation and creation operators [duplicate]
Most introductory quantum field theory books define Wick ordering as rearranging a product of creation and annihilation operators such that all the creation operators appear to the left of any ...
- 3,350
1
vote
0
answers
43
views
Normal ordering in Sine-Gordon model [duplicate]
I am studying Bosonization from Giamarchi's book (Quantum Physics in 1D), in Appendix E while doing RG analysis at second order he says (Eq. E.18) that we can NOT expand cosine directly because field $...
- 366
0
votes
1
answer
134
views
Wick's theorem and Feynman propagator
(this is the image from book 'No nonsense QFT' by Jakob Schwichtenberg, page no, 426)
The quantity $[\phi_-(x),\phi_+(y)]$ is like an operator inside the bra-kets $\langle 0|$ and $|0\rangle$.
I'm not ...
- 69
1
vote
0
answers
43
views
Time-ordering operators: Can we simplify expressions inside? [duplicate]
Clearly if we have two operators $\phi(t_1)$ and $\psi(t_2)$ and define a time ordering operator $T$ acting on operators such that $$T(\phi(t_1)\psi(t_2)):=\phi(t_1)\psi(t_2),~\text{if $t_1>t_2$ ...
- 838
1
vote
2
answers
269
views
Using Wick's theorem on already normal-ordered functions
The book Quantum Field Theory of Many Body systems (X. G. Wen) defines Wick's theorem as follows.
I would like to employ this definition to simplify the 4-operator product $$\hat{O}\;=\;a_p^\dagger ...
1
vote
1
answer
78
views
How one can use Wick's theorem for the product $A:\mathrel{B^{n}}:$?
I try to use Wick's theorem in the case that some products we deal with are already normal ordered.
My guess is that it could be something like
\begin{equation}
A:\mathrel{B^{n}}:~=~:\mathrel{AB^{n}}:+...
- 155