基于诱生物质想法的五维Dirac方程

Five-dimension Dirac Equation in Induced-matter Theory

根据 Wesson-Liu诱生物质的想法 ,典型粒子的静质量可通过 Kaluza-Klein型理论约化到四维空时而获得 .通过引入附加维的动量算符并把它认同于静质量本征值算符而将 Dirac方程推广到五维共形不变形式 .当约化到四维空时时得到类似通常形式的 Dirac方程 ,粒子静质量对弯曲空时是随空时坐标变化的 .具体求解了五维宇宙学问题 。

According to the idea of the Wesson-Liu induced-matter, the rest mass of a typical particle is obtained by reducing Kaluza-Klein type theory to 4D space. Dirac equation is generalized to 5D conformally invariant form by introducing extra-dimension momentum operator identified with the rest mass eigenvalue operator. The normal Dirac equation is gained by reducing the generalization to four-dimension space. The rest mass of a particle in curve space vary with the space and time coordinates. A class of exact cosmological solution of the apparently empty 5D Kaluza-Klein field equations is derived . The conclusion is checked reasonable for the static spherically symmetric gravity and the close cosmological model.