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Currently the proven theory is the quantum field theory. This theory defines fields in "all spacetime" and particles are disturbances in these fields. These particles are punctual and interact through virtual particles.

But string theory is not clear to me. This defines the strings (bosonic or fermionic) as the smallest entities and these "strings are in a spacetime" but they are not defined unlike the fields in all spacetime. How is it possible? How is the zero point energy then described? So we must understand that at every point in space there is at least one section of string?

Here the difference is analogous to the first quantization with the second quantization. Is a string field already confirmed in all string theories? Is there talk of virtual strings?

If I take a field, for example the Dirac field or the EM field, these are defined in all time space. It may be that there are disturbances that we interpret as particles, but if there are not, the field exists the same and has a zero field energy value not equal to zero, with virtual particles being created and destroyed. Or for example, the higgs field directly has a non-zero energy in all space. Do we have a defined string in all space?

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  • $\begingroup$ What do you mean by "but they are not defined unlike the fields in all space time"? $\endgroup$
    – Prahar
    Commented May 4, 2023 at 13:44
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    $\begingroup$ If I take a field, for example the Dirac field or the EM field, these are defined in all time space. It may be that there are disturbances that we interpret as particles, but if there are not, the field exists the same and has a zero field energy value not equal to zero, with virtual particles being created and destroyed. Or for example, the higgs field directly has a non-zero energy in all space. On the ropes? Do we have a defined chord in all space? $\endgroup$
    – JAOdev
    Commented May 4, 2023 at 13:50
  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented May 4, 2023 at 14:08

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Field theory is not the only way to describe quantum particles (though I would argue that it is the best way) -- you can also use the worldline formalism which is more clanky, but does the job equally well. The worldline formalism is a first quantized formulation and field theory is second quantized.

The standard formulation of string theory generalizes the worldline formalism to a worldsheet formalism. This is what students learn when they take a course on string theory. It is a first quantized formulation.

There also exists a second quantized formulation ("QFT-like") of string theory known as string field theory. This formulation has only been understood recently (though the idea dates back to the 90s) so it is not usually taught in a course and its not something you learn unless you plan to do research on this topic.

Some good texts for each of these things above are:

QFT: Peskin & Schroeder, Weinberg Vol 1-3, Schwartz, Srednicki, and many many more.

World-line formulation of QFT: https://indico.cern.ch/event/206621/attachments/317309/442801/lectures_morelia_CS.pdf

Worldsheet String theory: Polchinski, Green-Schwarz-Witten, Becker-Becker-Schwarz, Kiritsis, etc.

String Field theory: https://arxiv.org/abs/2301.01686

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  • $\begingroup$ Thank you. But STF is a logical formulation, that is, necessary to describe the quantum states of the vacuum? That is, is the first quantization of the strings studied as a first approach to then continue with the SFT theory? Because it is understandable that having extensions with 2 parameters solves the problems of infinities that point particles have, but it continues with that formalism working with individual objects and nature has or shows at least one aspect that in all space-time never is empty and therefore there are fields. $\endgroup$
    – JAOdev
    Commented May 4, 2023 at 14:45
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    $\begingroup$ @JAOdev - It depends on what questions you are interested in. For most questions people study now, the first quantized formalism is enough. For some newer questions such as entanglement entropy or moduli stabilization or tachyon condensation, one needs an off-shell formalism and string field theory is used there. I do not understand your comment about "extensions with 2 parameters". The problems of infinities are dealt with by renormalization as usual. That is not a matter of concern either in QFT or in string theory. $\endgroup$
    – Prahar
    Commented May 4, 2023 at 15:33

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