| Speaker: | Federico Mattei
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Title: |
From 3-geometry transition amplitudes to graviton states |
| Abstract: |
In various background independent approaches, quantum gravity is
defined in terms of a field propagation kernel: a sum over paths interpreted
as a transition amplitude between 3-geometries, expected to project quantum
states of the geometry on the solutions of the Wheeler-DeWitt equation. We
study the relation between this formalism and conventional quantum field
theory methods. We consider the propagation kernel of 4d Lorentzian general
relativity in the temporal gauge, defined by a conventional formal Feynman
path integral, gauge fixed �la Fadeev-Popov. If space is compact, this
turns out to depend only on the initial and final 3-geometries, while in the
asymptotically flat case it depends also on the asymptotic proper time. We
compute the explicit form of this kernel at first order around flat space,
and show that it projects on the solutions of all quantum constraints,
including the Wheeler-DeWitt equation, and yields the correct vacuum and
n-graviton states. We also illustrate how the Newtonian interaction is
coded into the propagation kernel, a key open issue in the spinfoam
approach.
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| Talk: |
Transparencies, Recorded Talk
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