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Quantum Theory as an Emergent Phenomenon : The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory - Stephen L. Adler

Quantum Theory as an Emergent Phenomenon

The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory

Hardcover Published: 1st August 2004
ISBN: 9780521831949
Number Of Pages: 238

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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 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 recent phenomenological proposals for stochastic modifications to Schrodinger dynamics.

"This is a bold book, a provocative text, that may help many readers to have a better understanding of the foundations of quantum theories." American Mathematical Society "The book describes in detail a rich mathematical framework out of which a new physical description of nature can emerge. The chapters are well organized; the presentation is clear, rigorous, very attractive, and accessible to mathematical as well as theoretical physicists. It is recommended to everyone who wants to learn more about the fascinating field of the foundations of physics and the continuing efforts scientists are making to formulate a clear and coherent picture of physical phenomena." - Angelo Bassi, Universitat Munchen

Acknowledgementsp. x
Introduction and overviewp. 1
The quantum measurement problemp. 2
Reinterpretations of quantum mechanical foundationsp. 6
Motivations for believing that quantum mechanics is incompletep. 9
An overview of this bookp. 13
Brief historical remarks on trace dynamicsp. 18
Trace dynamics: the classical Lagrangian and Hamiltonian dynamics of matrix modelsp. 21
Bosonic and fermionic matrices and the cyclic trace identitiesp. 21
Derivative of a trace with respect on an operatorp. 24
Lagrangian and Hamiltonian dynamics of matrix modelsp. 27
The generalized Poisson bracket, its properties, and applicationsp. 29
Trace dynamics contrasted with unitary Heisenberg picture dynamicsp. 32
Additional generic conserved quantitiesp. 39
The trace "fermion number" Np. 39
The conserved operator Cp. 42
Conserved quantities for continuum spacetime theoriesp. 52
An illustrative example: a Dirac fermion coupled to a scalar Klein-Gordon fieldp. 58
Symmetries of conserved quantities under p[subscript F left and right arrow] q[subscript F]p. 62
Trace dynamics models with global supersymmetryp. 64
The Wess-Zumino modelp. 64
The supersymmetric Yang-Mills modelp. 67
The matrix model for M theoryp. 70
Superspace considerations and remarksp. 72
Statistical mechanics of matrix modelsp. 75
The Liouville theoremp. 76
The canonical ensemblep. 81
The microcanonical ensemblep. 88
Gauge fixing in the partition functionp. 93
Reduction of the Hilbert space modulo i[subscript eff]p. 100
Global unitary fixingp. 106
The emergence of quantum field dynamicsp. 117
The general Ward identityp. 119
Variation of the source termsp. 124
Approximations/assumptions leading to the emergence of quantum theoryp. 128
Restrictions on the underlying theory implied by further Ward identitiesp. 139
Derivation of the Schrodinger equationp. 147
Evasion of the Kochen-Specker theorem and Bell inequality argumentsp. 151
Brownian motion corrections to Schrodinger dynamics and the emergence of the probability interpretationp. 156
Scenarios leading to the localization and the energy-driven stochastic Schrodinger equationsp. 157
Proof of reduction with Born rule probabilitiesp. 170
Phenomenology of stochastic reduction--reduction rate formulasp. 174
Phenomenology of energy-driven reductionp. 175
Phenomenology of reduction by continuous spontaneous localizationp. 185
Discussion and outlookp. 190
Appendicesp. 193
Modifications in real and quaternionic Hilbert spacep. 194
Algebraic proof of the Jacobi identity for the generalized Poisson bracketp. 194
Symplectic structures in trace dynamicsp. 198
Gamma matrix identities for supersymmetric trace dynamics modelsp. 201
Trace dynamics models with operator gauge invariancep. 204
Properties of Wightman functions needed for reconstruction of local quantum field theoryp. 206
BRST invariance transformation for global unitary fixingp. 208
Referencesp. 212
Indexp. 220
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9780521831949
ISBN-10: 0521831946
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 238
Published: 1st August 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.4 x 17.0  x 1.4
Weight (kg): 0.58