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Physics

Questions tagged [s-matrix-theory]

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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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I am working on a problem about Cutkosky’s cutting rule in Matt D. Schwartz’s Quantum Field Theory and the Standard Model. The problem asks us to show that the imaginary part of the amplitude is given ...
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I've been trying to understand quantum scattering, but I think I am not very clear about the full picture in the derivation of differential cross-section below. In Modern Quantum Mechanics by Sakurai, ...
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So by my understanding, all the particles known to exist are either spin 1, 1/2 or 0. While I don't follow the details, I've also heard the spin-statistics theorem's conclusion that in 3+1D spacetime, ...
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I am trying to compute the Feynman rules for a theory with derivative coupling:$$\mathscr{L}_{int} = e v^{\mu} (\partial_{\mu} \phi) \phi$$where $\phi$ is a real, massive scalar field, and $v^{\mu}...
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The standard Cutkosky rules go as follows:Cut the appropriate propagators (replace them with $(-2\pi i) \delta(p^2-m^2)$).Sum over all cuts.This gives $\operatorname{Im}$ (I am dropping factors ...
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ContextIt is well known that $S$-matrix could be computed in the following two ways:Calculate in interaction picture Perturbatively.Use the LSZ reduction.To be specific, we have the math ...
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Consider a general Euclidean QFT (or its lattice regularization).Given a list of all correlators of operators in this theory, and given that they are reflection-positive, how can one explicitly ...
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I'm reviewing the derivation of the LSZ formalism and I'm comfortable with the position-space version, which has the following form:$$\left<{p_i};{\rm out}|{q_j};{\rm in}\right> = i^{n+m}\int \...
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I've been trying for a while to prove how Peskin and Schroeder come up with formula 7.57 in their book (reported in the image below). But I cannot seem to understand how to derive the result. Moreover ...
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I am currently trying to understand the derivation of the LSZ reduction formula showed in the Book "Introduction to Quantum Field Theory" by Peskin and Schroeder. Here eq. (7.36) states:$$...
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I'm trying to prove the LSZ reduction formula for fermions, but I'm having some issues with signs.In particular, I found this reference that seems to use the following identities at the end of page 2:...
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In QM the probability is violated when:$\int \rho(\vec r,t)\vec dr\neq 1$ for a quantum mechanical system in an arbitrary state $\psi(\vec r,t)$.In this case we know that $\psi(\vec r,t)$ is the ...
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I have read about the Cutkosky cutting rules and optical theorem when I was studying for theoretical particle physics. I.e. Imaginary part of Greens function is directly correlated to the sum of decay ...
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In equation 4.87 of Peskin & Schroeder it states,$$\langle p_{1}p_{2}...|S\left|k_{A}k_{B}\right\rangle = \lim_{T\rightarrow \infty}\langle p_{1}p_{2}...|e^{-iH(2T)}\left|k_{A}k_{B}\right\rangle\...
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I am currently reading Weinberg The Quantum Theory of Fields, chapter $3$. Consider the following superpositions of states;\begin{equation}|\Psi_g^{\pm}(t)\rangle=\int\mathrm{d}\alpha \exp{(-iE_\...

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