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Quantum Gravity Grand Unification New Physics
Lecture Notes to DPG Spring Conferences
General Relativity Consistently Unified with Quantum Theory
Giving Quantum Gravity in Operator Notation + Dark Energy
C. Birkholz
presented at the joint DPG Spring Conf. on Particles, on Gravitation, on the Mathematics of Physics, and on the Philosophy of Physics,
Göttingen/Germany, GR 10.1 (2012)
This unification is achieved by group theory. The group SU(2,2) is identified to be the fully quantized covering group of (an extended form of) GR.
(1) Its linear generators yield quantum theory,
(2) Its non-linear Casimir operators create curvature,
(3) Irreducibility provides background independence.
Dark energy results as a byproduct of the commutation relations of the (non-linear) space-time operators. By the number 3 of Casimir operators in an SU(2,2), the equations of motion in GR are fixed to have three components (3-dimensionality of motion).
  A maximal set of commuting generators defining the "quantization axis" of GR is given by the triplet L3 (spin), Q3 (CMS-space), P0 (energy).