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arXiv 0803.2003gr-qc
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弯曲时空中的公理化量子场论

Axiomatic quantum field theory in curved spacetime

S. Hollands, R. M. Wald

摘要:

闵可夫斯基时空中的量子场论通常的表述都使用了闵可夫斯基时空非常特殊的特征,比如庞加莱不变性和优先真空态的存在。为了将量子场论的表述推广到任意全局双曲弯曲时空,理论必须以完全局域和协变的方式表述,而不假设存在优选态。我们提出了一个新的量子场论框架,其中算子乘积展开(OPE)的存在性被提升到一个基本的地位,从本质上讲,量子场论的所有性质都是由它的OPE决定的.我们提供了量子场论的OPE系数的一般公理。这些假设包括局域和协方差假设(这意味着量子场论是由时空度规局域和协变地构造的)、微局域谱条件、“结合性”条件,以及场与其伴随场的乘积在OPE中的恒等系数具有正标度的要求。我们证明了弯曲时空版本的自旋统计定理和PCT定理。讨论了我们的新观点对量子场论的一些潜在意义。

英文摘要:

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.

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