Linear spin-zero quantum fields in external gravitational and scalar fields
Linear spin-zero quantum fields in external gravitational and scalar fields
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外部引力场和标量场中的线性自旋零量子场
DOI：
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发表时间：
1980
期刊：
影响因子：
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通讯作者：
B. S. Kay
中科院分区：
文献类型：
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作者：
B. S. Kay
讨论了弯曲时空中线性场和相互作用场的量子理论。本文论证了一般弯曲时空情形迫使量子场论采用代数方法，并提出了一种适用于处理任意整体双曲时空中任意准自由态的形式.对于相互作用情形，这些准自由态被作为合适的起点，在微扰理论中，场算符乘积的期望值可以计算到任意阶.微扰理论中对相互作用场的形式处理被归结为“自由”量子场与外部源相互作用的处理。该方法的核心是所谓的双电流算符，它用无源理论的纯代数(即表示自由)性质来描述外部源的影响。文章最后给出了一组似乎特别适合弯曲时空的“费曼规则”，因为它处理了问题中特定于弯曲时空(且与相互作用无关)的那些方面。启发式地，该方案计算的是“in-in”而不是“in-out”矩阵元素。重整化问题被讨论了，但没有被处理。
The quantum theory of both linear, and interacting fields on curved space-times is discussed. It is argued that generic curved space-time situations force the adoption of the algebraic approach to quantum field theory: and a suitable formalism is presented for handling an arbitrary quasi-free state in an arbitrary globally hyperbolic space-time.For the interacting case, these quasi-free states are taken as suitable starting points, in terms of which expectation values of field operator products may be calculated to arbitrary order in perturbation theory. The formal treatment of interacting fields in perturbation theory is reduced to a treatment of “free” quantum fields interacting with external sources.Central to the approach is the so-called two-current operator, which characterises the effect of external sources in terms of purely algebraic (i.e. representation free) properties of the source-free theory.The paper ends with a set of “Feynman rules” which seems particularly appropriate to curved space-times in that it takes care of those aspects of the problem which are specific to curved space-times (and independent of interaction). Heuristically, the scheme calculates “in-in” rather than “in-out” matrix elements. Renormalization problems are discussed but not treated.