QUANTUM FIELDS IN CURVED SPACE-TIMES
QUANTUM FIELDS IN CURVED SPACE-TIMES
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DOI：
10.1098/rspa.1975.0181
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发表时间：
1975-01-01
期刊：
影响因子：
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通讯作者：
MAGNON, A
中科院分区：
文献类型：
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作者：
ASHTEKAR, A;MAGNON, A
讨论了在给定的弯曲时空中获得（真实）克莱因戈登系统的量子描述的问题。使用代数方法。量子算子的*-代数被显式地构造，并且找到其*-表示的问题被简化为在（经典）克莱因-戈登方程的解的实向量空间上选择合适的复结构。由于在静态时空中已经存在令人满意的量子场论，在这种情况下，人们已经知道“正确”的复杂结构是什么。获得了这种“正确”复杂结构的物理表征。这种表征用于将量子场论扩展到非静态时空。首先考虑静止时空。在这种情况下，广延问题是完全简单的，由此产生的理论是静态时空理论的自然推广。然后考虑一般的非静止时空。在这种情况下，扩展问题相当复杂，我们只提出一个合理的扩展。尽管由此产生的框架在数学上有明确的定义，但与之相关的物理解释却相当非常规。讨论了该框架的优点和缺点。
The problem of obtaining a quantum description of the (real) KleinGordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is constructed explicitly and the problem of finding its *-representation is reduced to th at of selecting a suitable complex structure on the real vector space of the solutions of the (classical) Klein-Gordon equation. Since, in a static space-time, there already exists, a satisfactory quantum field theory, in this case one already knows what the ‘ correct ’ complex structure is. A physical characterization of this * correct ’ complex structure is obtained. This characterization is used to extend quantum field theory to nonstatic space-times. Stationary space-times are considered first. In this case, the issue of extension is completely straightforward and the resulting theory is the natural generalization of the one in static space-times. General, non-stationary space-times are then considered. In this case the issue of extension is quite complicated and we only present a plausible extension. Although the resulting framework is well-defined mathematically, the physical interpretation associated with it is rather unconventional. Merits and weaknesses of this framework are discussed.