LEADER 05158nam 2200685Ia 450 001 9910454264803321 005 20200520144314.0 010 $a1-281-86598-2 010 $a9786611865986 010 $a1-84816-142-5 035 $a(CKB)1000000000537743 035 $a(EBL)1681082 035 $a(OCoLC)815741824 035 $a(SSID)ssj0000227421 035 $a(PQKBManifestationID)11221886 035 $a(PQKBTitleCode)TC0000227421 035 $a(PQKBWorkID)10269841 035 $a(PQKB)10267585 035 $a(MiAaPQ)EBC1681082 035 $a(WSP)0000P235 035 $a(PPN)168237172 035 $a(Au-PeEL)EBL1681082 035 $a(CaPaEBR)ebr10255544 035 $a(CaONFJC)MIL186598 035 $a(EXLCZ)991000000000537743 100 $a20010404d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe principles of Newtonian and quantum mechanics$b[electronic resource] $ethe need for Planck's constant, h /$fM A de Gosson 210 $aLondon $cImperial College Press ;$aRiver Edge, NJ $cDistributed by World Scientific Pub.$dc2001 215 $a1 online resource (382 p.) 300 $aDescription based upon print version of record. 311 $a1-86094-274-1 320 $aIncludes bibliographical references (p. [343]-351) and index. 327 $aCONTENTS ; FOREWORD BY BASIL HILEY ; PREFACE ; 1 FROM KEPLER TO SCHRODINGER ... AND BEYOND ; 1.1 Classical Mechanics ; 1.2 Symplectic Mechanics ; 1.3 Action and Hamilton-Jacobi's Theory ; 1.4 Quantum Mechanics ; 1.5 The Statistical Interpretation of w 327 $a1.6 Quantum Mechanics in Phase Space 1.7 Feynman's ""Path Integral"" ; 1.8 Bohmian Mechanics ; 1.9 Interpretations ; 2 NEWTONIAN MECHANICS ; 2.1 Maxwell's Principle and the Lagrange Form ; 2.2 Hamilton's Equations ; 2.3 Galilean Covariance 327 $a2.4 Constants of the Motion and Integrable Systems 2.5 Liouville's Equation and Statistical Mechanics ; 3 THE SYMPLECTIC GROUP ; 3.1 Symplectic Matrices and Sp(n) ; 3.2 Symplectic Invariance of Hamiitonian Flows ; 3.3 The Properties of Sp(n) ; 3.4 Quadratic Hamiltonians 327 $a3.5 The Inhomogeneous Symplectic Group 3.6 An Illuminating Analogy ; 3.7 Gromov's Non-Squeezing Theorem ; 3.8 Symplectic Capacity and Periodic Orbits ; 3.9 Capacity and Periodic Orbits ; 3.10 Cell Quantization of Phase Space ; 4 ACTION AND PHASE ; 4.1 Introduction 327 $a4.2 The Fundamental Property of the Poincare-Cartan Form 4.3 Free Symplectomorphisms and Generating Functions ; 4.4 Generating Functions and Action ; 4.5 Short-Time Approximations to the Action ; 4.6 Lagrangian Manifolds ; 4.7 The Phase of a Lagrangian Manifold 327 $a4.8 Keller-Maslov Quantization 330 $a This book deals with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "principle of the symplectic camel", which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduc 606 $aLagrangian functions 606 $aMaslov index 606 $aGeometric quantization 608 $aElectronic books. 615 0$aLagrangian functions. 615 0$aMaslov index. 615 0$aGeometric quantization. 676 $a530.12 700 $aGosson$b Maurice de$067588 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454264803321 996 $aThe principles of Newtonian and quantum mechanics$92151681 997 $aUNINA