Cambridge University Press, Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, 2004. — 238 p.Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This book develops a new approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level is taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation–anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with recent phenomenological proposals for stochastic modifications to Schroedinger dynamics.Introduction and overview The quantum measurement problem Reinterpretations of quantum mechanical foundations Motivations for believing that quantum mechanics is incomplete An overview of this book Brief historical remarks on trace dynamics Trace dynamics: the classical Lagrangian and Hamiltonian dynamics of matrix models Bosonic and fermionic matrices and the cyclic trace identities Derivative of a trace with respect to an operator Lagrangian and Hamiltonian dynamics of matrix models The generalized Poisson bracket, its properties, and applications Trace dynamics contrasted with unitary Heisenberg picture dynamics Additional generic conserved quantities The trace “fermion number” N The conserved operator C Conserved quantities for continuum spacetime theories An illustrative example: a Dirac fermion coupled to a scalar Klein–Gordon field Symmetries of conserved quantities under p F <-> q F Trace dynamics models with global supersymmetry The Wess–Zumino model The supersymmetric Yang–Mills model The matrix model for M theory Superspace considerations and remarks Statistical mechanics of matrix models The Liouville theorem The canonical ensemble The microcanonical ensemble Gauge fixing in the partition function Reduction of the Hilbert space modulo i eff Global unitary fixing The emergence of quantum field dynamics The general Ward identity Variation of the source terms Approximations/assumptions leading to the emergence of quantum theory Restrictions on the underlying theory implied by further Ward identities Derivation of the Schroedinger equation Evasion of the Kochen–Specker theorem and Bell inequality arguments Brownian motion corrections to Schroedinger dynamics and the emergence of the probability interpretation Scenarios leading to the localization and the energy-driven stochastic Schroedinger equations Proof of reduction with Born rule probabilities Phenomenology of stochastic reduction – reduction rate formulas Phenomenology of energy-driven reduction Phenomenology of reduction by continuous spontaneous localization Discussion and outlook Modifications in real and quaternionic Hilbert space Algebraic proof of the Jacobi identity for the generalized Poisson bracket Symplectic structures in trace dynamics Gamma matrix identities for supersymmetric trace dynamics models Trace dynamics models with operator gauge invariance Properties of Wightman functions needed for reconstruction of local quantum field theory BRST invariance transformation for global unitary fixing
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