论文标题
de Sitter Spacetime中量化Dirac场的一般协变理论
A Generally Covariant Theory of Quantized Dirac Field in de Sitter Spacetime
论文作者
论文摘要
作为我们以前的工作\ cite {feng2020}的续集，我们在本文中提出了一种dirac field de Sitter SpaceTime的量化方案。我们的计划在一般变换和洛伦兹变换下都是协变量的。我们首先提出了哈密顿结构，然后按照受约束系统的标准方法对场进行量化。对于自由场，时间依赖性的量化哈密顿量是通过Bogliubov转换对角度对角线的，并且每个瞬间的特征园被解释为当时观察到的粒子状态。观察到的粒子/反粒子的可测量能量与Klein-Gordon场相同。此外，能量摩托车还满足地测量方程，这是一种证明其可测量性的功能。如\ cite {feng2020}中，尽管为了方便起见，数学是按照层坐标进行的，但整个理论可以基于一般协方差将整个理论转化为任何其他坐标。得出的结论是，粒子/反粒子状态，尤其是真空状态，尤其是时间依赖性和真空状态，并在以后会演变为非vacuum状态。扰动计算的形式主义带有扩展的狄拉克图片。
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present a Hamiltonian structure, then quantize the field following the standard approach of constrained systems. 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 measurable energy-momentum of observed particle/antiparticles are the same as obtained for Klein-Gordon field. Moreover, the energy-momentum also satisfies geodesic equation, a feature justifying its measurability. As in \cite{Feng2020}, though the mathematics is carried out in terms 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/antiparticle 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 calculation is provided with an extended Dirac picture.
