All Questions
10 questions
1vote
0answers
207views
Discontinuity of the scattering amplitude and optical theorem
The generalized optical theorem is given by: \begin{equation}\label{eq:optical_theorem} M(i\to f) - M^*(f\to i) = i \sum_X \int d\Pi_X (2\pi)^4 \delta^4(p_i-p_X)M(i\to X)M^*(f\to X).\tag{Box 24.1} ...
- 63
2votes
1answer
141views
Scattering Amplitude & Unitarity
In Srednicki's Quantum Field Theory chapter 11, the probability of a $2 \to n$ scattering process is calculated to be $$ P = \frac{|\left<f|i\right>|^2}{\left<f|f\right>\left<i|i\right&...
- 168
1vote
1answer
874views
Unitarity and amplitudes
In Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory there are few statements about analytical structure of amplitudes. I want to understand statement: In a local theory of ...
- 5,757
2votes
1answer
480views
Deriving Unitarity of $S$-matrix in 1D Quantum Mechanics
I was studying about scattering across a one-dimensional unknown potential ( pretty elementary Quantum Mechanics) and how, if we know the $S$-matrix of such a system, we can deduce an awful lot of ...
- 813
0votes
0answers
105views
Why can we use time-dependent perturbations when evaluating the S-matrix?
Suppose we have Hamiltonian $H_0 + V$. When working in the interaction picture we may derive the evolution operator of $|\psi_I(0)\rangle$ which is given by $$S(t,t_0) = T\left[\exp \left( -i \int_{...
- 238
0votes
0answers
273views
Show $S$-operator is unitary
In an exercise, we are supposed to show that the scattering matrix on the right of $$S_1(E)= \begin{pmatrix}t_1 & r_1' \\ r_1& t_1'\end{pmatrix}\delta(E_f-E_i)$$ is unitary. We are explicitly ...
- 417
7votes
1answer
1kviews
Positivity of residues and unitarity in scattering amplitudes
I am reading "Superstring Theory" by Green, Schwarz, Witten. In the introduction, about the Veneziano amplitude (below eq. 1.1.16/17), they say that The residues of poles must be positive in a ...
- 369
4votes
1answer
1kviews
Why does S-matrix unitarity imply the cross section $\sigma$ $\propto$ $\frac {1}{s}$?
I'm currently learning for an oral exam in theoretical physics and as a learning aid protocols of older exams exist. In one protocol the question was asked: Why is the scattering cross section $\...
- 10.4k
5votes
2answers
8kviews
Why are scattering matrices unitary?
In Griffith's QM book, he introduces scattering matrices as an end-of-the-chapter Problem 2.52. For a Dirac-Delta potential $V(x) = \alpha \delta (x - x_0)$, I've derived the scattering matrix and ...
- 1,791
5votes
3answers
3kviews
Unitarity of S-matrix in QFT
I am a beginner in QFT, and my question is probably very basic. As far as I understand, usually in QFT, in particular in QED, one postulates existence of IN and OUT states. Unitarity of the S-matrix ...
- 2,339
