EAN: 9783319773704

THE QUANTIZATION OF GRAVITY - CLAUS GERHARDT GE...

A unified quantum theory incorporating the four fundamental forces of nature is one of the
major open problems in physics. The Standard Model combines electro-magnetism  the strong force
and the weak force  but ignores gravity. The quantization of gravity is therefore a necessary
first step to achieve a unified quantum theory. In this monograph a canonical quantization of
gravity has been achieved by quantizing a geometric evolution equation resulting in a
gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of
separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint
operators where the temporal operator has a pure point spectrum with eigenvalues $lambda_i$ and
related eigenfunctions  while  for the spatial operator  it is possible to find corresponding
eigendistributions for each of the eigenvalues $lambda_i$  if the Cauchy hypersurface is
asymptotically Euclidean or if the quantized spacetime is a black hole with a negative
cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which
are products of temporal eigenfunctions and spatial eigendistributions. Due to this spectral
resolution of the wave equation quantum statistics can also be applied to the quantized
systems. These quantum statistical results could help to explain the nature of dark matter and
dark energy.

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