论文标题
旋转型二元性
Spin-orbit duality
论文作者
论文摘要
在四维平坦空间中提出了一种新的二元性，该空间在自旋和轨道自由度之间交换。这是由巨大田间角型摩托车型生物运动的杂物分解的动机，而旋转和轨道角动量彼此之间是霍奇双重双重的。二元性尊重poincarè对称性，并显示出在互补的间距区域之间的转化，将固定的三维de Sitter世界管（围绕质量中心）投射到大部分的四维时空，反之亦然。这种状况被解释为全息原则的实现。生存在该管上的双重理论原来是不交流性的，并且完全由庞加尔代数的卡西米尔元素定义。实际上，质量现在是紫外线的临界值。这自然表明，对于具有巨大的非零旋转领域的庞加莱或洛伦兹 - 不变性量子理论，时空是在基本级别进行量化的。
A new duality is proposed in four-dimensional flat space, which exchanges between spin and orbital degrees of freedom. This is motivated by a Hodge decomposition of the angular-momentum bivector for massive fields, along which spin and orbital angular momentum are Hodge duals of one another. The duality respects Poincarè symmetry and is shown to transform between complementary spacelike regions, projecting a fixed three-dimensional de Sitter world-tube (around the center of mass) into the bulk of four-dimensional spacetime and vice versa. This state of affairs is interpreted as a realization of the holographic principle. The dual theory living on that tube turns out to be noncommutative and entirely defined by the Casimir elements of the Poincarè algebra. In fact, the mass is now an ultraviolet cutoff. This naturally suggests that, for a Poincarè or just Lorentz-invariant quantum theory with massive fields of nonzero spin, spacetime is quantized at the fundamental level.
