03989nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001000172072001700182072002300199072001600222100008500238245007700323250001800400264006900418300004300487336002600530337002600556338003600582347002400618490005500642505041200697520174301109650001702852650002202869650002602891650004302917650003302960650004202993650002203035650002603057650005503083710003403138773002603172776003603198776003603234776003603270830006203306856004603368912001403414912001403428999001703442978-3-031-67922-3DE-He21320251030113259.0cr nn 008mamaa241106s2024    sz |    s    |||| 0|eng d  a97830316792239978-3-031-67922-37 a10.1007/978-3-031-67922-32doi 4aQC178 7aPHDV2bicssc 7aSCI0330002bisacsh 7aPHDV2thema1 aGerhardt, Claus.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98706914aThe Quantization of Gravityh[electronic resource] /cby Claus Gerhardt.  a2nd ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXII, 264 p. 1 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aFundamental Theories of Physics,x2365-6425 ;v1940 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.  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. 0aGravitation. 0aCosmology.976015 0aMathematical physics. 0aElementary particles (Physics).968885 0aQuantum field theory.96888614aClassical and Quantum Gravity.96940924aCosmology.97601524aMathematical Physics.24aElementary Particles, Quantum Field Theory.9688872 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303167921608iPrinted edition:z978303167923008iPrinted edition:z9783031679247 0aFundamental Theories of Physics,x2365-6425 ;v19497052340uhttps://doi.org/10.1007/978-3-031-67922-3  aZDB-2-PHA  aZDB-2-SXP  c64736d64736