LEADER 05233nam 2200709Ia 450 001 9910784876203321 005 20230607221501.0 010 $a981-277-837-3 035 $a(CKB)1000000000402915 035 $a(EBL)1679686 035 $a(OCoLC)855898964 035 $a(SSID)ssj0000136832 035 $a(PQKBManifestationID)11158687 035 $a(PQKBTitleCode)TC0000136832 035 $a(PQKBWorkID)10087661 035 $a(PQKB)10539422 035 $a(MiAaPQ)EBC1679686 035 $a(WSP)00004804 035 $a(Au-PeEL)EBL1679686 035 $a(CaPaEBR)ebr10201293 035 $a(CaONFJC)MIL505455 035 $a(EXLCZ)991000000000402915 100 $a20020618d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDeparametrization and path integral quantization of cosmological models$b[electronic resource] /$fClaudio Simeone 210 $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$dc2001 215 $a1 online resource (152 p.) 225 1 $aWorld scientific lecture notes in physics ;$vv. 69 300 $aDescription based upon print version of record. 311 $a981-02-4741-9 320 $aIncludes bibliographical references and index. 327 $aContents ; Preface ; Chapter 1 Introduction ; Chapter 2 The gravitational field as a constrained Hamiltonian system ; 2.1 Momentum and Hamiltonian constraints ; 2.2 Minisuperspaces as constrained systems ; 2.3 Quantization ; 2.3.1 Canonical quantization 327 $a2.3.2 Path integral quantization Chapter 3 Deparametrization and path integral quantization ; 3.1 The identification of time ; 3.1.1 Gauge fixation and deparametrization ; 3.1.2 Topology of the constraint surface: intrinsic and extrinsic time 327 $a3.2 Gauge-invariant action for a parametrized system 3.2.1 End point terms ; 3.2.2 Observables and time ; 3.2.3 Non separable constraints ; 3.3 Path integral ; 3.3.1 General formalism ; 3.3.2 The function f and the reduced Hamiltonian. Unitarity ; 3.4 Examples 327 $a3.4.1 Feynman propagator for the Klein-Gordon equation 3.4.2 The ideal clock ; 3.4.3 Transition probability for empty Friedmann-Robertson-Walker universes ; Chapter 4 Homogeneous relativistic cosmologies ; 4.1 Isotropic universes ; 4.1.1 A toy model ; 4.1.2 True degrees of freedom 327 $a4.1.3 A more general constraint 4.1.4 Extrinsic time. The closed ""de Sitter"" universe ; 4.1.5 Comment ; 4.2 Anisotropic universes ; 4.2.1 The Kantowski-Sachs universe ; 4.2.2 The Taub universe ; 4.2.3 Other anisotropic models ; Chapter 5 String cosmologies 327 $a5.1 String theory on background fields 330 $a The problem of time is a central feature of quantum cosmology: differing from ordinary quantum mechanics, in cosmology there is nothing "outside" the system which plays the role of clock, and this makes difficult the obtention of a consistent quantization. A possible solution is to assume that a subset of the variables describing the state of the universe can be a clock for the remaining of the system. Following this line, in this book a new proposal consisting in the previous identification of time by means of gauge fixation is applied to the quantization of homogeneous cosmological models. 410 0$aWorld Scientific lecture notes in physics ;$vv. 69. 606 $aQuantum gravity 606 $aSpace and time 606 $aPath integrals 606 $aGauge invariance 606 $aHamiltonian systems 615 0$aQuantum gravity. 615 0$aSpace and time. 615 0$aPath integrals. 615 0$aGauge invariance. 615 0$aHamiltonian systems. 676 $a523.1 700 $aSimeone$b Claudio$01473682 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784876203321 996 $aDeparametrization and path integral quantization of cosmological models$93686938 997 $aUNINA