德西特时空中量子化实Klein-Gordon场的一般协变理论
A Generally Covariant Theory of Quantized Real Klein-Gordon Field in de Sitter Spacetime
AI总结：
本文提出德西特时空中实Klein-Gordon场的一般协变量子化方案，通过vierbein实现协变性，利用Bogliubov变换对角化哈密顿量，揭示真空态随时间演化，并给出扩展Dirac图像的微扰论形式。
摘要：
本文提出了一种在德西特时空中对实Klein-Gordon场进行量子化的方案。我们的方案借助vierbein实现一般协变性，这在弯曲时空中通常对于旋量场是必要的。我们首先给出哈密顿结构，然后按照标准方法对场进行量子化。对于自由场，时间依赖的量子化哈密顿量通过Bogliubov变换对角化，每一瞬时的本征态被解释为该瞬时观测到的粒子态。这一解释得到了已知的宇宙学红移公式和自由场4-动量的壳上条件的支持。尽管为方便起见，数学推导采用共形坐标进行，但整个理论基于一般协变性可以变换到任何其他坐标系。结论是，粒子态，特别是真空态，是时间依赖的，某一时刻的真空态会演化成后来时刻的非真空态。我们还提供了扩展的Dirac图像下的微扰论形式。
英文摘要：
We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first present a Hamiltonian structure, then quantize the field following the standard approach. For the free field, the time-dependent quantized Hamiltonian is diagonalized by Bogliubov transformation and the eigen-states at each instant are interpreted as the observed particle states at that instant. The interpretation is supported by the known cosmological red-shift formula and the on-shell condition of 4-momentum for a free field. Though the mathematics is carried out in term of conformal coordinates for the sake of convenience, the whole theory can be transformed into any other coordinates based on general covariance. It is concluded that particle states, such as vacuum states in particular are time-dependent and vacuum states at one time evolves into non-vacuum states at later times. Formalism of perturbational is provided with an extended Dirac picture.
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