## Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field TheoryQuantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an 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 are 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 phenomenological proposals for stochastic modifications to Schrödinger dynamics. |

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### Contents

the classical Lagrangian and Hamiltonian dynamics of matrix models | 21 |

2 Additional generic conserved quantities | 39 |

3 Trace dynamics models with global supersymmetry | 64 |

4 Statistical mechanics of matrix models | 75 |

5 The emergence of quantum field dynamics | 117 |

6 Brownian motion corrections to Schrödinger dynamics and the emergence of the probability interpretation | 156 |

7 Discussion and outlook | 190 |

Appendices | 193 |

212 | |

220 | |

### Common terms and phrases

adjointness Adler algebra analog apparatus appear apply approximation argument assume assumption average bosonic c-number canonical ensemble Chapter classical commute complex components condition conserved consider constant constructed corresponding cyclic defined degrees of freedom derivative discussion dynamical variables effective elements emergent energy equations equations of motion evolution example expression fact factor fermionic fluctuations follows function gauge give given global unitary invariance Grassmann Hamiltonian Hilbert space identity ieff implies indices integration introduce involving leading matrix measure needed obey obtained operator parameter particle phase space physical polynomials probabilities properties quantities quantum field theory quantum mechanics quantum theory reduction relations requires respect restricted result rule Schr¨odinger self-adjoint side standard statistical stochastic structure symmetric tion trace dynamics trace Hamiltonian trace Lagrangian transformation underlying values vanishing variables variations vector Ward identities zero