I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module, however my question is that since elementary particles can be thought of as excitations in a field in QFT and likewise particles can also be thought of as vibrating strings in String theory, does this mean that the strings in String theory are actually troughs (like in waves) in there corresponding fields?
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2$\begingroup$ Your initial assumption is a long way wide of the mark. $\endgroup$– John RennieCommented Oct 29, 2014 at 6:14
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1$\begingroup$ @John Rennie-Hello John, U mean the assumption that strings are like fields or that that string theory is a new breed of QFT, I'm curious as to the specific flaw in my question? $\endgroup$– GammaRayCommented Oct 29, 2014 at 7:25
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$\begingroup$ I can't comment with any authority since I've only read introductory string theory stuff. However it is entirely unlike quantum field theory. It is one of the miracles of string theory that QFT emerges as a long range/low energy limit. So your question is basically meaningless. Sorry. $\endgroup$– John RennieCommented Oct 29, 2014 at 7:53
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1$\begingroup$ @JohnRennie there do exist corresponding diagrams to the Feynman diagrams of QFT though.benjaminjurke.net/show/string-theory $\endgroup$– anna vCommented Oct 29, 2014 at 9:03
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I figure that string theory is a new breed of QFT which looks at fields in terms of a network of strings and also incorporates gravity into its module,
You should read some reviews of what string theory is .
String theory rejects the idea of a point particle as the fundamental constituent of the theory, which is the central concept in quantum field theory. By introducing 1-dimensional, extended objects (and higher dimensional membranes in its further developments) this gives rise to a natural smallest scale in form of the string length.
The average size of this string is expected to be much smaller than the smallest sizes probed experimentally, currently 10^(−16) centimetre, and might be as small as the Planck length, which is of the order of 10^(−33) centimetre.
So when one studies string theory at low energies compared to the Planck scale, it becomes difficult to see that strings are extended objects—they behave effectively 0-dimensional, i.e. pointlike. With this perspective in mind, point-like quantum field theory can be regarded as a sort of effective theory for strings at low energies.
Italics mine.
however my question is that since elementary particles can be thought of as excitations in a field in QFT and likewise particles can also be thought of as vibrating strings in String theory, does this mean that the strings in String theory are actually troughs (like in waves) in there corresponding fields?
No, because, as the quote says above, the QFT particles are the limit of the strings at low energies . The corresponding fields are String field theories which are
a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a Feynman diagram-like expansion for string scattering amplitudes.
Creation and annihilation operators, which are used in QFT exist also in string field theories, it is just that instead of point particles one has one dimensional strings, so this idea of troughs is no go.
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$\begingroup$ "String theory rejects the idea of a point particle as the fundamental constituent of the theory, which is the central concept in quantum field theory." I have trouble with this statement: already QFT rejects point particles as fundamental, but has quantum fields as central concept. So both string theory and QFT reject point particles, but they do it in completely different ways. I think the major confusion for a laypeople (like me) is how either can be more fundamental than the other (especially, how quantum fields arise from strings). $\endgroup$ Commented Aug 30, 2023 at 20:25
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$\begingroup$ It is all in the mathematics that is used to model the data and everything has to be consistent in the formats. if they are modeling the same data. One has to learn mathematics, not just language, since mathematics is the "language " of physics. $\endgroup$– anna vCommented Aug 31, 2023 at 4:01
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$\begingroup$ Sure, in the end it is math (and I have no problem with that, I understand the math). But one also needs the right ontology, and that is (at least in my view) rarely communicated with any care. E.g. if strings are free floating objects, there could be a patch of space where there are no strings. But quantum fields permeate all of space without gaps. So how could fields arise from strings? There seems to be no amount of math that can explain this away, because it is not a mathematical problem, but perhaps a misunderstanding in the nature of the fundamental constituents. $\endgroup$ Commented Aug 31, 2023 at 9:25
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$\begingroup$ It is just mathematics, the new theories would be discarded as wrong if they would not mathematically meld into the old forms in the region of phase space they are valid. $\endgroup$– anna vCommented Aug 31, 2023 at 10:54