参数化Lagrange场论强涌现的公理化方案和整体存在定理
An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories
摘要：
在本文中，我们提出了一个公理化的概念之间的强涌现现象的场论取决于额外的参数，我们称之为参数化场论。我们提出了充分的条件，确保存在这样的现象之间的两个给定的拉格朗日理论。更确切地说，我们证明了拉格朗日场论线性依赖于一个额外的参数出现从每一个多元多项式理论评估的微分算子，有明确的格林函数（或者，更一般地说，有一个右逆在某些扩展的意义上）。作为一个激励性的例子，我们表明，从noncommutativy出现的重力现象，在一个真正的或复杂的标量场的背景下，可以恢复从我们的涌现定理。我们还表明，在同样的情况下，我们也可以期待互惠，即，非对易性可能来自引力。并对其他一些特殊情况进行了分析。
英文摘要：
In this paper we propose an axiomatization for the notion of strong emergence phenomenon between field theories depending on additional parameters, which we call parameterized field theories. We present sufficient conditions ensuring the existence of such phenomena between two given Lagrangian theories. More precisely, we prove that a Lagrangian field theory depending linearly on an additional parameter emerges from every multivariate polynomial theory evaluated at differential operators which have well-defined Green functions (or, more generally, that has a right-inverse in some extended sense). As a motivating example, we show that the phenomenon of gravity emerging from noncommutativy, in the context of a real or complex scalar field theory, can be recovered from our emergence theorem. We also show that, in the same context, we could also expect the reciprocal, i.e., that noncommutativity could emerge from gravity. Some other particular cases are analyzed.
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