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Pure connection formalism for gravity: Feynman rules and the graviton-graviton scattering | | Gianluca Delfino
; Kirill Krasnov
; Carlos Scarinci
; | | Date: |
23 Oct 2012 | | Abstract: | We continue to develop the pure connection formalism for gravity. We derive
the Feynman rules for computing the connection correlation functions, as well
as the prescription for obtaining the Minkowski space graviton scattering
amplitudes from the latter. The present formalism turns out to be significantly
simpler than the one based on the metric in many aspects. The most drastic
difference with the usual approach is that the conformal factor of the metric,
which is a source of difficulties in the metric treatment, does not propagate
in the connection formulation even off-shell. This simplifies both the
linearized theory and the interactions. For comparison, in our approach the
complete off-shell cubic GR interaction contains just 3 terms, with only a
single term relevant at tree level. This should be compared to at least a dozen
terms in the metric formalism. We put the technology developed to use and
compute the simplest graviton-graviton scattering amplitudes. For GR we
reproduce the well-known result. For our other, distinct from GR, interacting
theories of massless spin 2 particles we obtain non-zero answers for some
parity-violating amplitudes. Thus, in the convention that all particles are
incoming, we find that the 4 minus, as well as the 3 minus 1 plus amplitudes
are zero (as in GR), but the amplitudes with 4 gravitons of positive helicity,
as well as the 3 plus 1 minus amplitudes are different from zero. This serves
as a good illustration of the type of parity violation present in these
theories. We find that the parity-violating amplitudes are important at high
energies, and that a general parity-violating member of our class of theories
"likes" one helicity (negative in our conventions) more than the other in the
sense that at high energies it tends to convert all present gravitons into
those of negative helicity. | | Source: | arXiv, 1210.6215 | | Services: | Forum | Review | PDF | Favorites | |
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