All Questions
17 questions
0votes
1answer
84views
Dividing multi-particle states into a sum of states with particles of definite number
In Peskin & Schroeder's book (7.1 , p212) in the studying of the analytic structure of two-point correlation function, they generalize the completeness relationship of 1 particle states $$ \left( ...
- 726
19votes
2answers
1kviews
What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?
For background, I'm primarily a mathematics student, studying geometric Langlands and related areas. I've recently been trying to catch up on the vast amount of physics knowledge I'm lacking, but I've ...
- 191
1vote
0answers
46views
Prefactor to amplitude for massless fermions/massive bosons
I was reviewing some of my old notes and found this formula for a matrix elements between two states: $$ <f|S|i>= \delta_{fi} + [(2\pi)^4 \delta^4(P_f - P_i) \prod_{ext. fermion}\left(\frac{m}{...
1vote
1answer
160views
Understanding from $S$-Matrix to Feynman-Rules in scalar QFT [closed]
I am learning QFT at the moment and the process from defining the S-Matrix to deriving the feynman rules is in my opinion pretty complicated, since there are many different things to pay attention to. ...
- 527
4votes
2answers
192views
Are amplitudes for inverse processes related to each other?
The (generalized) optical theorem is presented in the book of Peskin and Schroeder (An introduction to Quantum Field Theory - chapter 7-Radiative Corrections:Some Formal Developments) as follows $-i (\...
5votes
1answer
194views
How to obtain (interacting) time-ordered correlation functions from the $S$-matrix - reverse of the LSZ formula?
The LSZ formula shows how to obtain the $S$-matrix elements from the time-ordered correlation functions of the interacting fields. I wonder if there is a reverse formula; that is, can we find the ...
- 1,744
0votes
2answers
439views
Peskin & Schroeder LSZ formula missing in- and out states
In Peskin and Schroeder the LSZ-formula is given as below where the states in the $S$-matrix element are fully interacting Heisenberg states. $$\begin{array}{l}\prod_{1}^{n} \int d^{4} x_{i} e^{i p_{i}...
- 498
4votes
1answer
336views
LSZ reduction formula vs Dyson's expansion
In quantum field theory, we have use perturbation series to compute the $S$-matrix elements. For example: $$S=1+\sum_{i=1}^\infty\frac{(-i/\hbar)^n}{n!}\int_{-\infty}^\infty...\int_{-\infty}^\infty T[...
- 909
1vote
1answer
289views
Different forms of the LSZ reduction formula
I'm studying Chapter 7 section 2 of Peskin and Schroeder on the LSZ reduction formula, on page 227 they write the LSZ reduction formula $$\tag{7.42}\prod_1^n \int d^4x_i e^{ip_i\cdot x_i}\prod_1^m\int ...
- 909
4votes
2answers
351views
Derivation in LSZ Reduction Formula
In deriving the LSZ formula, a crucial step is to show $$\langle|a_{p}^{\dagger}|\rangle=-i\int dx^0 \int \mathrm{d}^{3} x \partial_{0}\langle | e^{-i p\cdot x} \overleftrightarrow{\partial_{0}} \phi(...
- 381
5votes
1answer
613views
Resolution of the Identity in Quantum Field Theory
In Peskin and Schroder's QFT book, on page 212, eq.7.2, they use the completeness relation in a derivation involving the two-point correlation function: $$ \mathbf{1}=|\Omega\rangle\langle\Omega|+\...
- 1,505
2votes
1answer
462views
The relation between full Green's function and S-matrix
I'm learning Green's function in condensed matter. The full Green's function is defined as $$G(k_2,t_2;k_1,t_1) = \langle\Omega |T a_{k_1}(t_1)a_{k_2}^{\dagger}(t_2) |\Omega \rangle $$ The $\Omega$ is ...
- 189
3votes
1answer
1kviews
LSZ formula for initial and final one particle states
The LSZ formula for a real scalar field $\varphi$ is (Srednicki 5.24) $$ \left<f|i\right>=i^{n+n'}\int d^4x_1e^{ik_1x_1}(-\partial_1^2+m^2)...\\ \quad d^4x'_1e^{ik'_1x'_1}(-\partial_{1'}^2+m^2).....
- 193
3votes
1answer
264views
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 ...
1vote
1answer
958views
On the S-Matrix and correlation functions
I'm learning about interactions in QFT. My primary source has been the book "Quantum Field Theory For The Gifted Amateur" by Tom Lancaster. From there I've learned that in QFT one is ...
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