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Pure Connection Formalism for Gravity: Linearized Theory | | Gianluca Delfino
; Kirill Krasnov
; Carlos Scarinci
; | | Date: |
31 May 2012 | | Abstract: | We give a description of gravitons in terms of an SL(2,C) connection field.
The gauge-theoretic Lagrangian for gravitons is simpler than the metric one.
Moreover, all components of the connection field have the same sign in front of
their kinetic term, unlike what happens in the metric formalism. The
gauge-theoretic description is also more economic than the standard one because
the Lagrangian only depends on 8 components of the field per spacetime point as
compared to 10 in the Einstein-Hilbert case. Particular care is paid to the
treatment of the reality conditions that guarantee that one is dealing with a
system with a hermitian Hamiltonian. We give general arguments explaining why
the connection cannot be taken to be real, and then describe a reality
condition that relates the hermitian conjugate of the connection to its
(second) derivative. This is quite analogous to the treatment of fermions where
one describes them by a second-order in derivatives Klein-Gordon Lagrangian,
with an additional first-order reality condition (Dirac equation) imposed. We
find many other parallels with fermions, e.g. the fact that the action of
parity on the connection is related to the hermitian conjugation. Our main
result is the mode decomposition of the connection field, which is to be used
in forthcoming works for computations of graviton scattering amplitudes. | | Source: | arXiv, 1205.7045 | | Services: | Forum | Review | PDF | Favorites | |
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