REMARKS ON POSITIVE FREQUENCY AND HAMILTONIANS IN EXPANDING UNIVERSES
REMARKS ON POSITIVE FREQUENCY AND HAMILTONIANS IN EXPANDING UNIVERSES
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DOI：
10.1007/bf00756661
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发表时间：
1979-01-01
影响因子：
2.8
通讯作者：
FULLING, SA
中科院分区：
文献类型：
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作者：
FULLING, SA
我们严格审查的持久的信念，即弯曲时空中的量子场论的物理解释是通过引入粒子的概念，在每个时间的一些energylike运营商在当时的确切本征态。似乎这个原理的所有直接实现都存在模糊性，或者无法产生有限的粒子密度和可重正化的能量动量张量。对比安奇I型宇宙学模型进行了计算，该模型包含一个标量场φ，其方程包含项ξRφ。总能量的对角化表明了某种粒子的定义，然而，只有当π =1/6且宇宙是各向同性的时，才产生有限的粒子产生率。非正则哈密顿的对角化是一个足够宽松的处方，可以与几乎任何一个假设（包括一个确实产生物理上可接受的期望值的假设）保持一致，因此没有理论价值。一个显然成功的天真的方法，各向同性的情况下（为任何）被解释为一个无意识的第一近似绝热分析的概念，积极的频率。
We examine critically the persistent belief that the physical interpretation of a quantum field theory in curved space-time is to be found by introducing a notion of particles at each time in terms of the exact eigenstates of some energylike operator at that time. It seems that all straightforward implementations of this principle suffer from either ambiguity or failure to produce finite particle densities and renormalizable energy-momentum tensors. Calculations are done for a cosmological model of Bianchi type I, containing a scalar fieldφwhose equation includes the term ξRφ. Diagonalization of thetotal energysuggests a certain particle definition, which, however, yields a finite particle creation rate only when ξ=1/6 and the universe is isotropic. Diagonalization of acanonical Hamiltonianis a prescription loose enough to be made consistent with almost any ansatz (including one that does yield physically acceptable expectation values), hence of no theoretical value. An apparently successful naive approach to the isotropic case (for any ξ) is explained as an unconscious first approximation to an adiabatic analysis of the notion of positive frequency.