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arXiv 0911.5136math-phgr-qchep-thmath.MPquant-ph
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地方性原则。效力、命运和挑战

The Principle of Locality. Effectiveness, fate and challenges

Sergio Doplicher

摘要:

狭义相对论和量子力学融合在量子场论的关键原理--定域性原理中。我们回顾了它的"不合理的有效性“的一些例子(这在量子场论的局部可观测量的算子代数表述中表现得最好),在局部可观测量的结构中单独挖掘整体规范不变性的根源,至少对于纯质量理论;但是在这个框架中处理局部规范不变性原理仍然是一个问题。如果人们试图弄清楚定域性原理在描述基本粒子之间引力的理论中的命运,这个问题也会出现。这样,时空就应该获得普朗克尺度的量子结构,定域性原理就失去了。这是一个关键的开放问题,以解开替代在这样的理论,这是同样数学尖锐,并减少到局部性原则在更大的规模。除了探索它的命运,定域性原理的许多挑战仍然存在;其中,超选择结构和统计的分析也存在无质量粒子,并给出一个精确的数学公式的测量过程中的本地和相对论性条款;为此,我们概述了一个定性的情况下,避免EPR粒子。

英文摘要:

The Special Theory of Relativity and Quantum Mechanics merge in the key principle of Quantum Field Theory, the Principle of Locality. We review some examples of its ``unreasonable effectiveness'' (which shows up best in the formulation of Quantum Field Theory in terms of operator algebras of local observables) in digging out the roots of Global Gauge Invariance in the structure of the local observable quantities alone, at least for purely massive theories; but to deal with the Principle of Local Gauge Invariance is still a problem in this frame. This problem emerges also if one attempts to figure out the fate of the Principle of Locality in theories describing the gravitational forces between elementary particles as well. Spacetime should then acquire a quantum structure at the Planck scale, and the Principle of Locality is lost. It is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp and reduces to the Principle of Locality at larger scales. Besides exploring its fate, many challenges for the Principle of Locality remain; among them, the analysis of Superselection Structure and Statistics also in presence of massless particles, and to give a precise mathematical formulation to the Measurement Process in local and relativistic terms; for which we outline a qualitative scenario which avoids the EPR Paradox.

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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