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I understand that the strings in string theory are posited to be many, many orders of size smaller than say, a quark, electron or any other particle. But if this is so, how does the string "expand" to produce the gargantuan, by comparison, particle? Is this expansion caused by its vibrational pattern or is there another way by which the extremely small string manifests itself into a much larger object? I am, of course, under the impression that each "elementary" particle is generated by the vibrational pattern of only one individual string, i.e., one string produces one electron, etc.

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  • $\begingroup$ Particles like quarks and electrons are point-like (at least in mainstream QFT). So in fact, string are bigger than particles. That's why strings cure most UV divergences, because there is a fundamental UV cut-off. $\endgroup$
    – Adam
    Nov 1 '13 at 3:03
  • $\begingroup$ Thanks Adam. But you see, Brian Greene's book explains that strings are about Planck size, but particles themselves are many many orders larger than the Planck size. This is what I'm trying to unravel. $\endgroup$
    – user32016
    Nov 9 '13 at 21:47
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"Strings" correspond to relativist quantum fields, for instance a bosonic relativist quantum field $X^\mu(\sigma, \tau)$, with one spatial dimension $\sigma$ and one time dimension $\tau$, and with boundary conditions (different for open strings and closed strings). Quantum excitations of this field (particles) may have different spins , so these quantum excitations may represent different particles (for the same field). Strings may be understood as a countable set of harmonic oscillators labelled by $n, \mu$, with creation operators $\alpha_{-n}^\mu$. For instance, the simplest excitation of a open string is $\alpha_{-n}^\mu|0,k\rangle$, and this represents a particle of spin $1$ , momentum $k$, and polarization $\mu$.

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  • $\begingroup$ Thanks, Trimok. I'll have to digest your explanation and review my understanding of the string. $\endgroup$
    – user32016
    Nov 9 '13 at 21:49

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