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Related Links
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Keywords:
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string functional quantization, M-theory,
fractals, spacetime structure, string condensate.
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Project goals:
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to apply some results about the functional quantization
of a closed bosonic string to suggest some properties of the
small-scale spacetime structure.
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Project results:
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some essential elements of a non-perturbative
approach to the dynamics of extended objects are discussed in
connection with their relevance for the small scale spacetime
structure.
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Short Description.
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Functional string
quantization was developed by refining an early formulation
by T. Eguchi. We recall the precise meaning of this approach
to quantum string theory, concentrating in particular on "areal"
string variables, the string propagator and the string wave
functionals. From this point of view it is possible to draw
a relationship between M-theory and the quantum mechanics
of string loops. These concepts are instrumental to the discussion
of the functional Schroedinger equation of "loop quantum
mechanics"; its solutions enable us to derive the Uncertainty
Principle for strings as well as its principal consequence,
which is the fractalization of quantum spacetime. In connection
with this interesting issue, the structure of spacetime is
analyzed in terms of an effective lagrangian based on a covariant,
functional extension of the Ginzburg-Landau model of superconductivity.
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Additional material:
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