标题： 广义协变局域性原理——局部量子物理的新范式 显示英文标题

标题： The generally covariant locality principle -- A new paradigm for local quantum physics

摘要： 本文将介绍量子场论模型无关描述的一种新方法。 这一新方法的主要特征是以局域的方式纳入广义相对论的广义协变性原理，从而引出了“局域协变量子场论”的概念。 这样的局域协变量子场论可以通过协变函子来数学描述，这些函子定义在两个范畴之间：一方面是从具有等距嵌入作为态射的整体双曲时空范畴，另一方面是从具有单位单射* - 自同态作为态射的* - 代数范畴。 此外，在此框架下，局域协变量子场可以被描述为某些函子之间的自然变换。 通常的Haag-Kastler固定时空背景流形上的算符代数网及其背景时空等距群的协变自同构作用，可以从这种新方法中以特殊情形重新获得。 这种新方法的例子也有所概述。 如果一个局域协变量子场论满足时间片公理，则可以自然地将其与某些称为“相对柯西演化”的自同构作用联系起来，这些作用描述了量子场论对时空背景度规局部变化的动力学响应。 相对柯西演化的时空度规泛函导数被发现是一个无散量，它在一个例子中被证明具有局域协变量子场论的能量动量张量的意义。 此外，我们讨论了局域协变量子场论状态空间的函子性质，这些性质保证了局域确定性原理的有效性。 显示英文摘要

摘要： A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a "locally covariant quantum field theory". Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of *-algebras with unital injective *-endomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual Haag-Kastler framework of nets of operator-algebras over a fixed spacetime background-manifold, together with covariant automorphic actions of the isometry-group of the background spacetime, can be re-gained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the time-slice axiom, one can naturally associate to it certain automorphic actions, called ``relative Cauchy-evolutions'', which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics. The functional derivative of a relative Cauchy-evolution with respect to the spacetime metric is found to be a divergence-free quantity which has, as will be demonstrated in an example, the significance of an energy-momentum tensor for the locally covariant quantum field theory. Furthermore, we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness.