arXiv 1306.57192013-06hep-thquant-ph

有效场论中的多粒子关联、多粒子系统和熵

Multi-particle correlations, many particle systems, and entropy in effective field theories

Giorgio Torrieri

备注：: Improved and extended discussion

摘要：

我们讨论的治疗，在一个有效场论，在一个"大"系统内的多粒子相关性。我们表明，粗粒化的行为必然会引入违反幺正性的粒子数没有定义的状态的演变。对于一个相互作用的系统，这种幺正性破坏可以在“短”时间内从紫外尺度级联到红外尺度。因此，一个有效场论对于描述多粒子关联和相关的可观测量是非常不充分的，即使远离截止尺度$Λ$也是如此。我们还认为，如果系统是强耦合在$Λ$，比它的最终状态{\em在有效场论}（EFT）将出现作为最高熵的状态，如果只有低累积量和相关的EFT自由度的测量。启发式地，这可以作为一个解释"熵"是如何创建在一个量子场论（QFT）的微观幺正演化。最后，我们讨论这些考虑可能提供一个线索，即使在相对较小的系统，以及所谓的黑洞信息悖论的强子碰撞中的明显热化;我们认为，"悖论"很可能是使用超出其有效性域的有效理论的文物。

英文摘要：

We discuss the treatment, in an effective field theory, of multi-particle correlations within a "large" system. We show that the act of coarse-graining necessarily introduces violations of unitarity in the evolution of states where the particle number is not defined. For an interacting system, such unitarity violations can cascade from the ultraviolet scale to the infrared in a "short" time. Hence, an effective field theory will be grossly inadequate for describing multi-particle correlations and related observables, even far away from the cut-off scale $Λ$. We furthermore argue that if the system is strongly coupled at $Λ$, than its final state {\em in the Effective Field Theory} (EFT) will appear as the highest entropy state if only low cumulants and correlations of the EFT degrees of freedom are measured. Heuristically, this can serve as an explanation of how "entropy" is created in a microscopically unitary evolution of a Quantum Field Theory (QFT). We conclude by discussing how these considerations might provide a clue to the apparent thermalization in a hadronic collision even in comparatively small systems, as well as the so-called black hole information paradox; We argue the "paradoxes" are likely to be artifacts of using an effective theory beyond its domain of validity.

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