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# 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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### Scattering matrix elements for potential $q(x)$

Suppose I have S.E. with potential $q(x)$, which is known, how do I compute the scattering or S-matrix with respect to this potential? I've tried searching for non-trivial (i.e constant potential ...
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### Vacuum bubbles and LSZ reduction

Let me preface this by saying that I don't have an issue with this: $$\langle\Omega|T\phi_H\cdots\phi_H|\Omega\rangle = \frac{\langle 0|T\phi_I\cdots\phi_IS|0\rangle}{\langle 0|S|0 \rangle},$$ ...
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### How to tell whether a Feynman diagram is $t$-channel or $s$-channel by looking?

By looking at a diagram, how does one tell whether it represents a $s$-channel process or a $t$-channel process i.e., without finding the amplitude? I'm familiar with Mandelstam variables but I've ...
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### LSZ Reduction Formula

In Section 3.7.2 of Tong's QFT notes the LSZ reduction formula is briefly discussed. Essentially, this tells us that for S-matrix elements we can use the same momentum space Feynman rules as for ...
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### Computing S-Matrix Elements from Feynman Diagrams

In Peskin and Schroeder (PS), the Feynman rules for calculating correlation functions are first presented. Only terms involving all field contractions need to be considered. In Section 4.6, this is ...
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### Scattering, 4 point correlator, #distinct Feynman diagrams

In order to compute the scattering probability that two particles of type 1 (associated to $\phi_1(x)$) which come from the far past with the momenta $p_1$ and $p_2$, to scatter and evolve into two ...
161 views

### Orthogonality of matrix elements, trace techniques

I am currently reading Thomson's "Modern particle physics", and I have trouble understanding a concept that he somewhat gives for granted. Using Feynman rules, I am able to compute the matrix element ...
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### Quantum Field Theory in position space instead of momentum space?

What are the reasons why we usually treat Quantum Field Theory in momentum space instead of position space? Are the computations (e.g. of Feynman diagrams) generally easier and are there other ...
For example consider $2\to2$ scattering in scalar $\phi^4$ theory. When the in/out coming positions are fixed, it is easy to calculate in terms of contractions. When we fix the incoming / outgoing ...