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Related Links
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Keywords:
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closed string, kernel, propagator, functional
Schroedinger equation, area variables, loop space.
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Project goals:
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to obtain a description of closed strings (and
other extended objects) considering them as fundamental objects
and, thus, not focusing on the dynamics of their constituents
(points).
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Project results:
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determination and solution of the equation for
the dynamics of a free closed string in terms of area variables;
the propagator is obtained and it turns out to ba a function
of Pluecher coordinates describing the motion of the
string in loop space.
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Short Description.
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Starting from the Hamilton-Jacobi formalism, a connection
is drawn between the dynamics of a closed string and a description
in terms of a functional Schroedinger equation. This functional
wave equation is for the string what the Wheeler-de Witt equation
is for quantum gravity!
A solution for the functional wave equation, the string propagator,
is then derived. It describes the motion of a free string
but it does not provide information on the motion of the
points that constitute the string. Instead it describes the
motion of the shape (in loop space) as a whole. The
coordinates of the string are, indeed, area (Pluecker) coordinates,
namely the area of the projections of the closed string onto
the coordinate planes.
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Additional material:
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