All Questions
Tagged with quantum-field-theory s-matrix-theory
463
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Work of LSZ reduction formula
I want to know the mechanism of the LSZ reduction formula. The left side will have $\langle f|S|i\rangle$ and the right side has Fourier transform of $(\Box+m^2)$ times multiplication of Heisenberg ...
- 534
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143
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LSZ reduction formula for scalar field
I am using Schwartz QFT and the LSZ reduction formula at pp 70. The scalar field was written as
$$
\phi(x)=\phi(\vec{x}, t)=\int \frac{d^3 p}{(2 \pi)^3} \frac{1}{\sqrt{2 \omega_p}}\left[a_p(t) e^{-i p ...
- 534
2
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63
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Simplify calculation for matrix elements in quantum electrodynamics
So I am learning quantum field theory. At the moment I have a look at the interactions between electrons/positrons and photons, which is quantum electrodynamics. I want to calculate matrix elements of ...
- 505
3
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1
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96
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Why can we use the scattering matrix formula for decay rate?
The derivation of the scattering matrix $S_{\alpha\beta}$ requires the states to exist asymptoitcaly, why can we use it for a decay rate where clearly the decaying particles does not exist ...
- 41
3
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1
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162
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Scattering ${\cal M}$- and $S$-matrix
I am reading QFT book, like Introduction to QFT by Peskin and Schroeder, I would like to know conceptually what is the difference between $S$-matrix and invariant matrix element ${\cal M}$ in ...
- 326
3
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Finding the interaction vertices
Given a Lagrange density $$\mathcal{L} = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi - \frac{m^2}{2}\phi^2 - \frac{\lambda_3}{3!}\phi^3 - \frac{\lambda_4}{4!}\phi^4$$ where $\phi$ is a scalar field,...
- 298
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129
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Expanding ladder operators in terms of field operator
In the LSZ reduction formula for calculating the S-matrix of real scalar interacting fields, one of the crucial steps in the derivation is to write the annihilation operator as $$a(\vec{k})=i\int d^3\...
- 838
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84
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Proof of boost generator $K_0$ commute with $S$-matix in Weinberg QFT 1
In Weinberg QFT Vol.1, Weinberg defines a boost operator K when there exists an interaction $V$ as
$$\textbf{K}=\textbf{K}_0+\textbf{W}, \tag{3.3.20}$$
where $\textbf{W}$ is expected as a correction ...
- 21
4
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1
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172
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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 ...
- 1,669
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74
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Optical theorem for Feynman diagrams
I'm studying section 7.3 of Peskin and Schroeder. In the middle of page 232, the book says:
For our present purposes, let us define $M$ by the Feynman rules for perturbation theory. This allows us to ...
- 789
4
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2
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416
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Optical theorem Peskin and Schroeder
I'm trying to understand the optical theorem of Peskin and Schroeder
$$\tag{7.50} \text{Im} M(k_1,k_2\rightarrow k_1,k_2)=2E_{cm}p_{cm}\sigma_{tot}(k_1,k_2\rightarrow\text{anything})$$
which Peskin ...
- 789
3
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201
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Vacuum matrix elements
On page 87, section 7.2.3 titled Vacuum matrix elements of Quantum Field Theory and the Standard Model by Matthew Schwartz, the author writes that the vacuum state $|\Omega>$ is annihilated by the ...
- 904
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51
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Are all amplitudes evaluated on-shell?
In [1] the authors state that for a free scalar theory (eq 7) under field redefinition $\phi\rightarrow a_1 \phi^2 + a_2 \phi^3 + ...$:
"Once evaluated on-shell, the n-point tree-level ...
- 447
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1
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87
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Question about asymptotic assumption in LSZ reduction formula derivation
I have a silly question in derivation of LSZ reduction formular, I can go directly with the derivation until I found a assumption that I can't convince myself.
In the book Quantum Field Theory and the ...
4
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1
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541
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LSZ reduction formula in Peskin and Schroeder: How do we see that disconnected diagrams have incorrect pole structure?
In derivation of the LSZ reduction formula in Peskin and Schroeder, on page 227, the book says
Let us analyze the relation between the diagrammatic expansion of the scalar field four-point function ...
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