Timeline for Different kinds of S-matrices?
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| Feb 5, 2012 at 21:23 | comment | added | Squark | Take QCD for example. What S-matrix are we computing in perturbation theory? I assumed it is the "adiabatic" S-matrix since the asymptotic states are free quarks and gluons. However in the "fully interacting" S-matrix the asymptotic states are hadrons. So, is it the case that both kinds of S-matrix exist or is that the latter matrix is the only one which makes sense nonperturbatively? | |
| Feb 5, 2012 at 20:46 | comment | added | Luboš Motl | Dear @Squark, it depends on whether there are lines of marginal stability in the theory (values of couplings at which some stable external states cease to exist) etc. If the "adiabatic" prescription for the S-matrix works, then the $g\to 0$ and $g\to \infty$ Hilbert spaces of free particles are isomorphic and there is a simple isomorphism. Of course, if there exist asymptotic states but this existence depends on the finiteness of $g$, then the isomorphism of the two "free" Hilbert spaces breaks down: but your original adiabatic method won't work, anyway. | |
| Feb 5, 2012 at 18:35 | comment | added | Squark | But these matrices live in different spaces, since the free particle spectrum is different from the interacting particle spectrum and the spectra in different free limits are also different | |
| Feb 5, 2012 at 18:21 | history | answered | Luboš Motl | CC BY-SA 3.0 |