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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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### Why do we not have spin greater than 2?

It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also ...
5k views

### 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 ...
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### Relation between Borchers class and the LSZ formula on S-matrix equivalence

It seems well known that different quantum fields can give rise to the same $S$-matrix. I know of two ways this is described. The first is through the Borchers class of relatively local fields, i.e. ...
442 views

### Materials about S-matrix and S-matrix theory

What is the best book or paper to learn about analytical structures of S-matrix and S-matrix theory? I already know books as The Analytic S-matrix by RJ Eden, PV Landshoff, DI Olive, JC P and Quantum ...
61 views

### What justifies the use of asymptotic momentum state?

The LSZ scattering approach starts with initial and final asymptotic momentum states. But we know that $\langle k' | k\rangle = \delta^3(k'-k)$, which means that it is not a properly normalizable ...
I am reading from Schwarz book on QFT the Path Integral chapter and I am confused about something. I attached a SS of that part. So we have $$<\Phi_{j+1}|e^{-i\delta H(t_j)}|\Phi_{j}>=N \exp(i\... 1answer 72 views ### Condition for finitely many bound states in one dimension This came up in the context of the inverse scattering transform for the KdV equation. My primary reference, a set of lecture notes on integrable systems by Maciej Dunajski, makes the claim that the ... 1answer 75 views ### Do Reggeons-Pomerons-Odderons offer an Universal picture of hadron interactions? As far as I know, the total cross-sections of the following hadron interactions are well described by a single Reggeon trajectory and a single Pomeron (soft Pomeron) trajectory. It seems to work for ... 1answer 156 views ### How is scattering possible? Bjorken and Drell's book shows that the 'in' and 'out' states are eigenstates of the full interacting theory. If this is true, then how is scattering possible if both in and out states are eigenstates ... 1answer 292 views ### Green functions in QFT What is the sense of Green function$$ \langle | \hat {T}(u_{1}(x_{1})...u_{n}(x_{n})\hat {S})|\rangle , \quad \hat {S} = \hat{T}e^{i\int \hat {L}(x)d^{4}x} ?  How is it connected with scattering ...
In quantum mechanics, in the context of symmetry transformations, it is often said that for a transformation $T$ to conserve probabilities it must be unitary. But by performing any (even non-unitary)...