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arXiv quant-ph/0610204quant-phgr-qchep-thmath.LO
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无波函数的量子动力学

Quantum Dynamics without the Wave Function

Rafael D. Sorkin

摘要:

当适当地推广和解释,路径积分提供了一个替代更熟悉的量子形式主义的基础上状态向量,自伴算子,和外部观察员。在数学上,人们把作为传播子的路径积分推广为所有"可想象世界“的空间$Ω$上的{ \it量子测度} $μ$,这个推广的测度表示理论的动力学或运动定律,就像维纳测度表示布朗运动的动力学一样。在这种“以历史为基础”的方案中,为解决状态向量形式主义的哲学问题开辟了新的、更"现实的“可能性。特别是,通过将$μ$的预测内容定位在其测量零的集合中,可以免除对外部代理的需要:这样的集合将被"排除“。但是,不加限制地应用这一规则会产生矛盾。一种可能的对策是通过限制排除概念的适用来消除矛盾。另一种反应,更接近“量子逻辑”的传统,将通过把$Ω$二元论化为一个“共同事件”的空间,并有效地用这个对偶空间的一个元素来识别现实,来适应这些矛盾。

英文摘要:

When suitably generalized and interpreted, the path-integral offers an alternative to the more familiar quantal formalism based on state-vectors, selfadjoint operators, and external observers. Mathematically one generalizes the path-integral-as-propagator to a {\it quantal measure} $μ$ on the space $Ω$ of all ``conceivable worlds'', and this generalized measure expresses the dynamics or law of motion of the theory, much as Wiener measure expresses the dynamics of Brownian motion. Within such ``histories-based'' schemes new, and more ``realistic'' possibilities open up for resolving the philosophical problems of the state-vector formalism. In particular, one can dispense with the need for external agents by locating the predictive content of $μ$ in its sets of measure zero: such sets are to be ``precluded''. But unrestricted application of this rule engenders contradictions. One possible response would remove the contradictions by circumscribing the application of the preclusion concept. Another response, more in the tradition of ``quantum logic'', would accommodate the contradictions by dualizing $Ω$ to a space of ``co-events'' and effectively identifying reality with an element of this dual space.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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