where the two indices of each graviton labeled by
i
= 1, 2, 3 are
,
i.e.
.
Such relations, however, do not hold in any of the standard
formulations of gravity. For example, the three-vertex in the
standard de Donder gauge (3) contains traces over gravitons,
i.e.
a contraction of indices of a single graviton. For physical
gravitons the traces vanish, but for gravitons appearing inside
Feynman diagrams it is in general crucial to keep such terms. A
necessary condition for obtaining a factorizing three-graviton
vertex (4
) is that the ``left''
indices never contract with the ``right''
indices. This is clearly violated by the three-vertex in
Eq. (3
). Indeed, the standard formulations of quantum gravity generate
a plethora of terms that violate the heuristic relation (1
).
In Section
4
the question of how one rearranges the Einstein action to be
compatible with string theory intuition is returned to. However,
in order to give a precise meaning to the heuristic
formula (1) and to demonstrate that scattering amplitudes in gravity
theories can indeed be obtained from standard gauge theory ones,
a completely different approach from the standard Lagrangian or
Hamiltonian ones is required. This different approach is
described in the next section.
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Perturbative Quantum Gravity and its Relation to Gauge
Theory
Zvi Bern http://www.livingreviews.org/lrr-2002-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |