http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Cover; Contents; List of Figures; Acknowledgements; 1 Introduction; 1.1 Outline of Chapters; 1.2 Notation; 1.3 Shape Dynamics in a nutshell; Part I Historical Motivation; 2 Newton's Bucket; 2.1 The defects of the law of inertia; 2.2 Leibniz's relationalism; 2.3 The Scholium problem; Further reading; 3 Origins of the Machâ#x80;#x93;PoincarÃ© Principle; 3.1 Tait's partial solution of the Scholium problem; 3.2 Mach's critique of Newton; 3.3 Hoffman's experiment; 3.4 PoincarÃ©'s principle; Further reading; Part II Relational Particle Dynamics; 4 Barbourâ#x80;#x93;Bertotti Best Matching
4.1 Best matching: intuitive approachFurther reading; 5 Best Matching: Technical Details; 5.1 Mathematical Formulation; 5.2 Temporal relationalism: Jacobi's principle; 5.3 Best matching `in action'; Further reading; 6 Hamiltonian Formulation; 6.1 The Hamiltonian constraint; 6.2 A crash course in Dirac's constraint analysis; 6.3 Application to our systems; 6.4 A matter of units; Further reading; Part III Relational Field Theory; III.1 The Ontology of Fields; III.2 The origins of Geometrodynamics; III.3 An exercise in counterfactual history; III.4 Nuggets of functional analysis
7 Relativity Without Relativity7.1 Rigidity of the choice of the Lagrangian; 7.2 Inclusion of a scalar field: Special Relativity; 7.3 Inclusion of a one-form field: Gauge Theory; 7.4 Best-matching gauge transformations; 7.5 Yangâ#x80;#x93;Mills Theory; 7.6 Further generalizations; Further reading; 7.7 The problem of many-fingered time; 8 York's Solution to the Initial-Value Problem; 8.1 Lichnerowicz's partial solution; 8.2 York's general solution; Further reading; 9 A derivation of Shape Dynamics; 9.1 Analysis of Case III; Further reading; 10 Cotton-Squared Theory; Part IV Shape Dynamics
11 Historical Interlude12 Shape Dynamics and the Linking Theory; 12.1 Linking Theory's equation of motion; 12.2 The degrees of freedom of Shape Dynamics; 12.3 The solution to the problem of time in SD; 12.4 Coupling to matter and uniqueness; 12.5 Experienced spacetime; 12.6 `Symmetry doubling': BRST formulation of SD; 12.7 `Conformal geometrodynamics regained'; 13 Solutions of Shape Dynamics; 13.1 Homogeneous solutions: Bianchi IX; 13.2 Continuation through the singularity; 13.3 Spherically symmetric solutions; 13.4 Asymptotically flat Shape Dynamics; Part V Appendices
Appendix A Arnowittâ#x80;#x93;Deserâ#x80;#x93;Misner GravityA.1 The Arnowittâ#x80;#x93;Deserâ#x80;#x93;Misner (ADM) formalism; Further reading; A.2 The Wheelerâ#x80;#x93;DeWitt equation; A.3 The Baierleinâ#x80;#x93;Sharpâ#x80;#x93;Wheeler action; A.4 Asymptotically flat ADM; Appendix B Other Appendices; B.1 The case for closed spacelike hypersurfaces; B.2 Free-end-point variation; B.3 Lie derivative; B.4 TT decomposition of tensors; B.5 Point sources in ADM gravity; B.6 The poles of a spherically-symmetric universe; References; Index