Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Acknowledgements -- Introduction and overview -- 1 The quantum measurement problem -- 2 Reinterpretations of quantum mechanical foundations -- 2.1 Histories -- 2.2 Bohmian mechanics -- 2.3 The Ax-Kochen proposal -- 2.4 Everett's "many worlds" interpretation -- 3 Motivations for believing that quantum mechanics is incomplete -- 3.1 Historical precedent -- 3.2 The quantum measurement problem -- 3.3 What is the origin of "canonical quantization"? -- 3.4 Infinities and nonlocality -- 3.5 Unification of quantum theory with gravitation -- 3.6 The cosmological constant -- 3.7 A concrete proposal -- 4 An overview of this book -- 5 Brief historical remarks on trace dynamics -- 1 Trace dynamics: the classical Lagrangian and Hamiltonian dynamics of matrix models -- 1.1 Bosonic and fermionic matrices and the cyclic trace identities -- 1.2 Derivative of a trace with respect to an operator -- 1.3 Lagrangian and Hamiltonian dynamics of matrix models -- 1.4 The generalized Poisson bracket, its properties, and applications -- 1.5 Trace dynamics contrasted with unitary Heisenberg picture dynamics -- 2 Additional generic conserved quantities -- 2.1 The trace "fermion number" N -- 2.2 The conserved operator C -- 2.3 Conserved quantities for continuum spacetime theories -- 2.4 An illustrative example: a Dirac fermion coupled to a scalar Klein-Gordon field -- 2.5 Symmetries of conserved quantities under… -- 3 Trace dynamics models with global supersymmetry* -- 3.1 The Wess-Zumino model -- 3.2 The supersymmetric Yang-Mills model -- 3.3 The matrix model for M theory -- 3.4 Superspace considerations and remarks -- 4 Statistical mechanics of matrix models -- 4.1 The Liouville theorem -- 4.2 The canonical ensemble -- 4.3 The microcanonical ensemble -- 4.4 Gauge fixing in the partition function*.

4.5 Reduction of the Hilbert space modulo ieff -- 4.6 Global unitary fixing* -- 5 The emergence of quantum field dynamics -- 5.1 The general Ward identity -- 5.2 Variation of the source terms -- 5.3 Approximations/assumptions leading to the emergence of quantum theory -- 5.4 Restrictions on the underlying theory implied by further Ward identities -- 5.5 Derivation of the Schrödinger equation -- 5.6 Evasion of the Kochen-Specker theorem and Bell inequality arguments -- 6 Brownian motion corrections to Schrödinger dynamics and the emergence of the probability interpretation -- 6.1 Scenarios leading to the localization and the energy-driven stochastic Schrödinger equations -- 6.2 Proof of reduction with Born rule probabilities -- 6.3 Phenomenology of stochastic reduction - reduction rate formulas -- 6.4 Phenomenology of energy-driven reduction -- 6.5 Phenomenology of reduction by continuous spontaneous localization -- 7 Discussion and outlook -- Appendices -- Appendix A: Modifications in real and quaternionic Hilbert space -- Appendix B: Algebraic proof of the Jacobi identity for the generalized Poisson bracket -- Appendix C: Symplectic structures in trace dynamics -- Appendix D: Gamma matrix identities for supersymmetric trace dynamics models -- Appendix E: Trace dynamics models with operator gauge invariance -- Appendix F: Properties of Wightman functions needed for reconstruction of local quantum field theory -- Appendix G: BRST invariance transformation for global unitary fixing -- References -- Index.