## Born's Reciprocal General Relativity Theory and Complex Nonabelian Gravity as Gauge Theory of the Quaplectic Group : A novel path to Quantum Gravity

**Authors:** Carlos Castro

Born's Reciprocal Relativity in flat spacetimes is based on the principle of a
maximal speed limit (speed of light) and a maximal proper force (which is also
compatible with a maximal and minimal length duality) and where coordinates
and momenta are unified on a single footing. We extend Born's theory to the case of
curved spacetimes and construct a Reciprocal General Relativity theory (in curved
spacetimes) as a local Gauge Theory of the Quaplectic Group and given by the semidirect
product Q(1, 3) x U(1, 3)
sH(1, 3), where the Nonabelian Weyl-Heisenberg
group is H(1, 3). The gauge theory has the same structure as that of Complex
Nonabelian Gravity. Actions are presented and it is argued why such actions based
on Born's Reciprocal Relativity principle, involving a maximal speed limit and a
maximal proper force, is a very promising avenue to Quantize Gravity that does
not rely in breaking the Lorentz symmetry at the Planck scale, in contrast to other
approaches based on deformations of the Poincare algebra, Quantum Groups. It
is discussed how one could embed the Quaplectic gauge theory into one based on
the U(1, 4),U(2, 3) groups where the observed cosmological constant emerges in a
natural way. We conclude with a brief discussion of Complex coordinates and Finsler
spaces with symmetric and nonsymmetric metrics studied by Eisenhart as relevant
closed-string target space backgrounds where Born's principle may be operating.

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 5 Dec 2007

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