Statistical Dynamics of Global Unitary Invariant Matrix Models as Pre-Quantum Mechanics

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dc.creatorAdler, Stephen L.
dc.date2002-06-13
dc.date.accessioned2026-07-07T04:13:41Z
dc.date.available2026-07-07T04:13:41Z
dc.descriptionWe consider the classical dynamics of bosonic and fermionic matrix variables in complex Hilbert space, defined by a trace action, assuming cyclic invariance under the trace and the presence of a global unitary invariance. With plausible and explicitly stated assumptions, including the existence of a large hierarchy of scale between the underlying dynamics and observed physics, we show that (1) the equilibrium statistical mechanics of this matrix dynamics, in the canonical ensemble, gives rise to an emergent quantum mechanics for many degrees of freedom, including the standard canonical commutation/anticommutation relations and the usual unitary Heisenberg and Schrödinger picture time evolutions of operators and states, and (2) the fluctuation or Brownian motion corrections to this thermodyamics lead to an energy-driven stochastic modification of the Schrödinger equation, which is known to imply state vector reduction with Born rule probabilities. Thus, quantum mechanics and its probabilistic interpretation both arise as emergent phenomena in the underlying trace dynamics.
dc.descriptionDraft of a book; 175 pages in TeX. Comments welcome; revisions as needed will be made around 10/1/02
dc.identifierhttps://arxiv.org/abs/hep-th/0206120
dc.identifierhttp://arxiv.org/abs/hep-th/0206120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/51349
dc.subjectHigh Energy Physics - Theory
dc.subjectCondensed Matter
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleStatistical Dynamics of Global Unitary Invariant Matrix Models as Pre-Quantum Mechanics
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