John Baez
October 29, 2004
The Problem of Dynamics in Quantum Gravity
The problem of dynamics in quantum gravity
is still a big challenge. We don't know how to make spacetime
into a truly dynamical entity with local degrees of freedom
while taking quantum theory into account. Neither string
theory, nor loop quantum gravity, nor the spin foam and
causal dynamical triangulation approaches have yet found
a background-free quantum theory with
local degrees of freedom propagating causally.
We sketch some avenues for making progress in this direction.
Click on this to see the transparencies:
Here are some of the papers alluded to in this talk:
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Jan Ambjørn, J. Jurkiewicz and Renate Loll,
Emergence of a 4d world from causal quantum gravity
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John Baez, J. Daniel Christensen, Thomas Halford and David Tsang,
Spin foam models of Riemannian quantum gravity
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John Baez, J. Daniel Christensen and Greg Egan,
Asymptotics of 10j symbols
-
Etera Livine and Daniele Oriti,
Causality in spin foam models for quantum gravity
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Daniele Oriti,
The Feynman propagator for spin foam quantum gravity
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Andrzej Okolow and Jerzy Lewandowski,
Automorphism covariant representations of the holonomy-flux *-algebra
-
Hanno Sahlmann and Thomas Thiemann,
On the superselection theory of the Weyl algebra for diffeomorphism
invariant quantum gauge theories
-
Hanno Sahlmann and Thomas Thiemann,
Irreducibility of the Ashtekar-Isham-Lewandowski representation
-
Artem Starodubtsev,
Topological excitations around the vacuum of quantum gravity I:
The symmetries of the vacuum
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Lee Smolin and Artem Starodubtsev,
General relativity with a topological phase: an action principle
I also mentioned some work that has not yet appeared on the arXiv.
The work of Joshua Willis on no-go theorems for spin networks
with compact gauge group has not yet appeared, nor has the work
of my student Miguel Carrión Álvarez on Wilson loop
dynamics in quantum electromagnetism:
this is his PhD thesis, which should be finished by the
end of this year! The work of Laurent Freidel and Artem Starodubtsev
on 4d quantum gravity as a perturbation of a TQFT has also not
appeared yet, but it's foreshadowed in the papers by Starodubtsev
listed above. Finally, the so-called "LOST theorem"
is the work of Lewandowski, Okolow, Sahlmann and Thiemann. This
result has not yet appeared in its entirety, so its name is a
pun, but aspects of it can be found in the papers by these authors
listed above.
I also wrote an issue of This Week's Finds
about this conference: week208.
© 2004 John Baez
baez@math.removethis.ucr.andthis.edu