论文标题
量子模型用于时空度量的la gabor
Quantum models a la Gabor for space-time metric
论文作者
论文摘要
作为GABOR信号处理的扩展，实施了协变量Weyl-Heisenberg积分量化，以在八维相空间上转换函数$ \ left（x，k \ right）$中的函数。 $ x = \ left（x^μ\右）$是时空变量，$ k = \ left（k^μ\右）$作为Gabor信号处理的扩展，协证的weyl-heisenberg积分量化已实现，以在八维相位空间$ \ eft fiht（x，k k，k k，k，k k，k k \ hel fimply量）上实现了函数。 $ x = \ left（x^μ\右）$是时空变量，$ k = \ left（k^μ\ right）$是他们的共轭波向量频率变量。该过程首先应用于变量$ \ left（x，k \ right）$，并产生规范共轭的本质上是自动接合操作员。接下来是应用于一般相对论的公制$ g_ {μν}（x）$，并产生正则化的半经典相位空间肖像$ \ check {g} _ {μν}（x）$。后者产生了修改的张量能密度。用均匀加速的参考系统和Schwarzschild指标给出了示例。讨论了有趣的概率方面。
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space $\left(x,k\right)$ into Hilbertian operators. The $x=\left(x^μ\right)$'s are space-time variables and the $k=\left(k^μ\right)$'s are As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space $\left(x,k\right)$ into Hilbertian operators. The $x=\left(x^μ\right)$'s are space-time variables and the $k=\left(k^μ\right)$'s are their conjugate wave vector-frequency variables. The procedure is first applied to the variables $\left(x,k\right)$ and produces canonically conjugate essentially self-adjoint operators. It is next applied to the metric field $g_{μν}(x)$ of general relativity and yields regularised semi-classical phase space portraits $\check{g}_{μν}(x)$. The latter give rise to modified tensor energy density. Examples are given with the uniformly accelerated reference system and the Schwarzschild metric. Interesting probabilistic aspects are discussed.
