LEADER 04138nam 22006735 450 001 9910903795603321 005 20250808090325.0 010 $a9783031679223 010 $a3031679229 024 7 $a10.1007/978-3-031-67922-3 035 $a(MiAaPQ)EBC31755849 035 $a(Au-PeEL)EBL31755849 035 $a(CKB)36514425700041 035 $a(OCoLC)1468688097 035 $a(DE-He213)978-3-031-67922-3 035 $a(EXLCZ)9936514425700041 100 $a20241106d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Quantization of Gravity /$fby Claus Gerhardt 205 $a2nd ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (269 pages) 225 1 $aFundamental Theories of Physics,$x2365-6425 ;$v194 311 08$a9783031679216 311 08$a3031679210 327 $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. 330 $aA unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a hyperbolic equation in a fiber bundle, where the base space represents a Cauchy hypersurface of the quantized spacetime and the fibers the Riemannian metrics in the base space. The hyperbolic operator, a second order partial differential operator, acts both in the fibers as well as in the base space. In this second edition new results are presented which allow the solutions of the hyperbolic equation to be expressed as products of spatial and temporal eigenfunctions of self-adjoint operators. These eigenfunctions form complete bases in appropriate Hilbert spaces. The eigenfunctions depending on the fiber elements are a subset of the Fourier kernel of the symmetric space SL(n,R)/SO(n), where n is the dimension of the base space; they represent the elementary gravitons corresponding to the degrees of freedom in choosing the entries of Riemannian metrics with determinants equal to one. These are all the degrees of freedom available because of the coordinate system invariance: For any smooth Riemannian metric there exists an atlas such that in each chart the determinant of the metric is equal to one. In the important case n=3 the Standard Model could also be incorporated such that one can speak of a unified quantization of all four fundamental forces of nature. 410 0$aFundamental Theories of Physics,$x2365-6425 ;$v194 606 $aGravitation 606 $aCosmology 606 $aMathematical physics 606 $aParticles (Nuclear physics) 606 $aQuantum field theory 606 $aClassical and Quantum Gravity 606 $aCosmology 606 $aMathematical Physics 606 $aElementary Particles, Quantum Field Theory 615 0$aGravitation. 615 0$aCosmology. 615 0$aMathematical physics. 615 0$aParticles (Nuclear physics) 615 0$aQuantum field theory. 615 14$aClassical and Quantum Gravity. 615 24$aCosmology. 615 24$aMathematical Physics. 615 24$aElementary Particles, Quantum Field Theory. 676 $a530.1 700 $aGerhardt$b Claus$0835565 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910903795603321 996 $aQuantization of Gravity$91867663 997 $aUNINA