All Questions
31
questions
2
votes
1
answer
88
views
How is dimensionality of $S$ preserved term by term in a perturbative expansion?
In a schematic notation, the scattering matrix element $$\langle p_{out}|S|p_{in}\rangle := 1 + i (2 \pi)^4 \delta^4(p_{in} -p_{out}) M$$ between an incoming state with momentum $|p_{in}\rangle$ and ...
- 307
2
votes
1
answer
321
views
Weinberg, Effective Field Theories
Weinberg in his QFT Volume 1 points out in Chapter 12, section 12.3, near Fig. 12.4 (Is Renormalizability necessary?) that for expansions in EFTs in powers of $k/M$, where $k$ is the energy scale of ...
- 433
2
votes
2
answers
301
views
Renormalization and virtual soft divergences
I am reading Weinberg's book on QFT. Specifically, chapter 13.2. The author calculates the effect of including infrared quantum corrections (i.e. associated with soft virtual photons) to amplitudes. ...
- 3,992
5
votes
0
answers
243
views
LSZ formula in Srednicki, normalization issue
In the Ch.5 of his book, Srednicki says LSZ formula is valid provided the following conditions hold:
$$
\langle 0|\phi(x)|0\rangle = 0, \langle p|\phi(x)|0\rangle = 1
$$
To achieve these conditions, ...
- 51
3
votes
1
answer
244
views
The interpretation of the quantum field
In QM we have always been told that for each quantum mechanical field there is an associated particle. This works in the free theory where from canonical quantisation we promote a field to a field ...
- 766
1
vote
0
answers
99
views
In the derivation of LSZ formula, why do we need $\langle k| \phi(0)|0 \rangle =1$? (Srednicki's book)
In the section 5 of the book, it says
The LSZ formula is valid provided that the field obeys
$$\langle 0|\phi(x)|0\rangle=0, \langle k|\phi(x)|0\rangle=1.$$
The second one is needed to ensure one-...
- 995
2
votes
0
answers
107
views
Energy Renormalization and Vacuum Diagrams
I have been reading the lecture notes of Coleman's course on QFT. When developing scattering theory with the use of a cutoff function, he mentions that, in order to ensure that the free vacuum ...
- 3,915
4
votes
2
answers
537
views
Rescaling/renormalisation of the $n$-point function in $\phi^4$-theory by an unique $Z$?
In the chapter 12.2 of Peskin & Schroeder they introduce the rescaled renormalised $n$-point function respectively Green's function:
$$\langle \Omega|T\phi(x_1)\phi(x_2)\ldots \phi(x_n)|\Omega\...
- 9,778
4
votes
0
answers
389
views
Scattering amplitudes and LSZ formula for off-shell renormalization scheme
TLDR: The question: Does it make sense to calculate scattering amplitudes using an off-shell renormalization scheme?
I expand a bit by using a theory of a single self interacting massive scalar. I ...
- 1,129
2
votes
1
answer
1k
views
Why the Feynman diagram with loops attached to external legs is irrelevant to the $T$-matrix?
Hello friends I was stumbled when I learnt the scattering theory from textbook titled "Quantum Field Theory for the Gifted Amateur", which has related the scattering probability to the ...
- 132
4
votes
1
answer
232
views
Why are the renormalisation constants the same in LSZ and renormalisation?
To keep it simple I'll phrase everything in terms of scalar fields. We seem to have three constants called $Z$:
When we do LSZ reduction we say, as $t\rightarrow-\infty$ then $\phi\rightarrow \sqrt{...
- 1,933
5
votes
1
answer
184
views
Do all unitary-preserving regulators necessarily turn real loop integrals into pure imaginary numbers?
The optical theorem, which results from the unitarity of the $S$-matrix, relates the imaginary part of the forward scattering amplitude to the total cross section. When using this theorem in practice, ...
- 103k
1
vote
1
answer
285
views
QFT in in the asymptotic region
Let $\phi(x)$ be a scalar field operator. It often postulate in text books that in the asymptotic region we have
$$\lim_{x_0\to-\infty} \phi(x)=\sqrt Z \phi_{in}(x)$$
where $Z$ is a constant.
The ...
- 445
1
vote
1
answer
190
views
(Coleman's lecture note) scattering in QFT
I am currently reading Coleman's lecture note on QFT.(https://arxiv.org/abs/1110.5013) I have several questions regarding the scattering theory. Let $\phi$ be a real scalar field, and consider the ...
- 1,081
1
vote
0
answers
158
views
A Question about In/Out States in Quantum Field Theory
When I was reading the lecture notes Advanced Quantum Field Theory by Jorge Crispim Romao, I accidentally found the following thing that I don't understand.
On page 56, section 2.2, the author ...
- 2,923