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020 _a9783031679223
_9978-3-031-67922-3
024 7 _a10.1007/978-3-031-67922-3
_2doi
050 4 _aQC178
072 7 _aPHDV
_2bicssc
072 7 _aSCI033000
_2bisacsh
072 7 _aPHDV
_2thema
100 1 _aGerhardt, Claus.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_987069
245 1 4 _aThe Quantization of Gravity
_h[electronic resource] /
_cby Claus Gerhardt.
250 _a2nd ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXII, 264 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aFundamental Theories of Physics,
_x2365-6425 ;
_v194
505 0 _aThe quantization of a globally hyperbolic spacetime -- Interaction of gravity with Yang-Mills and Higgs fields -- The quantum development of an asymptotically Euclidean Cauchy hypersurface -- The quantization of a Schwarzschild-AdS black hole -- The quantization of a Kerr-AdS black hole -- A partition function for quantized globally hyperbolic spacetimes with a negative cosmological constant -- Appendix.
520 _aA 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 hyperbolic equation in a fiber bundle, where the base space represents a Cauchy hypersurface of the quantized spacetime and the fibers the Riemannian metrics in the base space. The hyperbolic operator, a second order partial differential operator, acts both in the fibers as well as in the base space. In this second edition new results are presented which allow the solutions of the hyperbolic equation to be expressed as products of spatial and temporal eigenfunctions of self-adjoint operators. These eigenfunctions form complete bases in appropriate Hilbert spaces. The eigenfunctions depending on the fiber elements are a subset of the Fourier kernel of the symmetric space SL(n,R)/SO(n), where n is the dimension of the base space; they represent the elementary gravitons corresponding to the degrees of freedom in choosing the entries of Riemannian metrics with determinants equal to one. These are all the degrees of freedom available because of the coordinate system invariance: For any smooth Riemannian metric there exists an atlas such that in each chart the determinant of the metric is equal to one. In the important case n=3 the Standard Model could also be incorporated such that one can speak of a unified quantization of all four fundamental forces of nature.
650 0 _aGravitation.
650 0 _aCosmology.
_976015
650 0 _aMathematical physics.
650 0 _aElementary particles (Physics).
_968885
650 0 _aQuantum field theory.
_968886
650 1 4 _aClassical and Quantum Gravity.
_969409
650 2 4 _aCosmology.
_976015
650 2 4 _aMathematical Physics.
650 2 4 _aElementary Particles, Quantum Field Theory.
_968887
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031679216
776 0 8 _iPrinted edition:
_z9783031679230
776 0 8 _iPrinted edition:
_z9783031679247
830 0 _aFundamental Theories of Physics,
_x2365-6425 ;
_v194
_970523
856 4 0 _uhttps://doi.org/10.1007/978-3-031-67922-3
912 _aZDB-2-PHA
912 _aZDB-2-SXP
999 _c64736
_d64736