We discuss a novel framework for physical theories that is based on the principles of locality and operationalism. It generalizes and unifies previous frameworks, including the standard formulation of quantum theory, the convex operational framework and Segal's approach to quantum field theory. It is capable of encoding both classical and quantum (field) theories, implements spacetime locality in a manifest way and contains the complete modern notion of measurement in the quantum case. Its mathematical content can be condensed into a set of axioms that are similar to those of Atiyah and Segal. This is supplemented by two basic rules for extracting probabilities or expectation values for measurement processes. The framework, called the positive formalism, is derived in three completely different ways. One derivation is from first principles, one starts with classical field theory and one with quantum field theory. The latter derivation arose previously in the programme of the general boundary formulation of quantum theory. As in the convex operational framework, the difference between classical and quantum theories essentially arises from certain partially ordered vector spaces being either lattices or anti-lattices. If we add the ad hoc ingredient of imposing anti-lattice structures, the derivation from first principles may be seen as a reconstruction of quantum theory. Among other things, the positive formalism suggests a statistical approach to classical field theories with dynamical metric, provides a common ground for quantum information theory and quantum field theory, introduces a notion of local measurement into quantum field theory, and suggests a new perspective on quantum gravity by removing the incompatibility with general relativistic principles.

中文翻译：

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物理学基础的局部和操作框架

我们讨论了基于局域性和操作主义原则的物理理论的新框架。它概括和统一了以前的框架，包括量子理论的标准公式、凸运算框架和西格尔的量子场论方法。它能够编码经典和量子（场）理论，以明显的方式实现时空局域性，并包含完整的现代测量概念在量子情况下。它的数学内容可以浓缩为一组与 Atiyah 和 Segal 相似的公理。为测量过程提取概率或期望值的两个基本规则对此进行了补充。该框架称为实证形式主义，它以三种完全不同的方式推导出来。一个推导来自第一性原理，一种从经典场论开始，一种从量子场论开始。后一个推导出现在量子理论的一般边界公式程序中。与凸运算框架一样，经典理论和量子理论之间的差异本质上源于某些部分有序的向量空间是格子或反格子。如果我们加上强加反晶格结构的特殊成分，那么从第一性原理推导出来就可以看作是对量子理论的重构。除其他外，正形式主义提出了一种具有动力学度量的经典场论的统计方法，为量子信息论和量子场论提供了共同基础，将局部测量的概念引入量子场论，