Statistical Dynamics of Global Unitary Invariant Matrix Models as Pre-Quantum Mechanics
Statistical Dynamics of Global Unitary Invariant Matrix Models as Pre-Quantum Mechanics
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作为前量子力学的全局酉不变矩阵模型的统计动力学
DOI：
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发表时间：
2002
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通讯作者：
S. Adler
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作者：
S. Adler
我们认为经典的玻色子和费米子矩阵变量在复杂的希尔伯特空间，定义的跟踪行动，假设循环不变性下的跟踪和存在的全球酉不变性。通过合理的和明确的假设，包括在基础动力学和观测物理之间存在一个大的尺度层次，我们证明了：（1）在正则系综中，这个矩阵动力学的平衡统计力学产生了一个多自由度的涌现量子力学，包括标准的正则对易/反对易关系以及算符和态的通常的酉海森堡和薛定谔图像时间演化，（2）对这种热力学的涨落或布朗运动修正导致薛定谔方程的能量驱动的随机修正，这意味着状态矢量用玻恩规则概率约化。因此，量子力学及其概率解释都是作为底层迹动力学中的涌现现象而出现的。
We 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 Schr"odinger 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 Schr"odinger 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.