# Questions tagged [s-matrix-theory]

The S-matrix (scattering matrix) relates the initial state and the final state of a physical system undergoing a scattering process in quantum mechanics and quantum field theory. It is the unitary matrix connecting asymptotic particle states in the Hilbert space of physical states (scattering channels).

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### Particle Creation by a Source

I am currently self-studying Quantum Field Theory and am using the textbook Introduction to Quantum Field Theory by Peskin and Schroeder. Currently I am in chapter 4, and am doing the first problem in ...
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### Scalar Electrodynamics or QED?

What's the difference between doing calculations in scalar electrodynamics and QED? I've seen that some people use scalar electrodynamics for Compton scattering and someone else using QED to solve for ...
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### On which propagator does the field self-contraction loop go on this Feynman diagram?

This question relates to page 111 in Peskin and Schroeder. I am trying to do the derivation of the 2-particle to 2-particle Feynman diagrams in $\phi^4$ theory by hand, following Peskin and Schroeder. ...
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This relates to page 111 in Peskin and Schroeder. We have the $\phi^4$ S-matrix for a 2-particle to 2-particle scattering reaction: $$-i\frac{\lambda}{4!}\int d^4x \langle p_1p_2|\mathcal T\left(\phi(... 1answer 54 views ### Why is there a negative sign in the time evolution operator when defining in/out states (Peskin/Schroeder) This relates to Peskin & Schroeder's QFT book, equation 4.70 on page 104. To define in and out states we take our initial state and evolve it far into the past, and do the same for our final state.... 0answers 55 views ### Has it been proven that causality means the S-matrix is analytic? In books like 'the analytic S-matrix' they give justification that causality implies analyticity however they also said it hasn't been explicitly proven. This book was written a while ago, has it been ... 1answer 151 views ### What does QFT say about non-linear processes? In QFT one can use the S matrix theory. We have a IN free system in the far past. It interacts in a black box in the present and there is a free OUT system in the far future. We have OUT = S IN with ... 1answer 73 views ### Prove that the scattering operator is unitary [duplicate] Let H_0 be some initial time-independent hamiltonian, and let V be a scattering potential, such that the hamiltonian of a scattering process is:$$H=H_0+V Define the quantum states $|\psi_i\... 0answers 57 views ### Why do we demand that symmetries commute with$S\$-matrix?

I am working in the context of Wightman Quantum Field Theory, and under a symmetry group I understand a group together with a unitary projective representation on the projective Hilbert space, unitary ...
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### Satisfying the equation of motion of the time evolution operator

In Cohen-Tannoudji's Atom-Photon Interactions, he gives the integral form of the time evolution operator in the Schrodinger representation as \begin{equation} U(t_{f},t_{I}) = U_{0}(t_{f},t_{i}) + \...