Gravitationally coupled Dirac equation for antimatter
Gravitationally coupled Dirac equation for antimatter
复制标题
反物质的引力耦合狄拉克方程
DOI：
10.1103/physreva.87.032101
复制
发表时间：
2013
影响因子：
2.9
通讯作者：
U. Jentschura
中科院分区：
文献类型：
--
作者：
U. Jentschura
反物质与引力的耦合引起了普遍的兴趣，因为可以想象到与暗能量和宇宙常数有关的宇宙学后果（“惊喜”）。在这里，我们重新推导引力耦合狄拉克方程，发现以前在[D. R.布里尔和J.A.惠勒，修订版模块物理学，Vol.29，p.465（1957）]的仿射连接矩阵需要校正。我们还讨论了从东海岸到西海岸的曲空间狄拉克方程的转换，以使引力耦合狄拉克方程的形式，它可以很容易地统一与电磁耦合，因为它是常用的现代粒子物理计算。狄拉克方程将反粒子描述为负能态。我们发现了引力耦合狄拉克方程的对称性，它连接了史瓦西型一般时空度规的粒子和反粒子解，并意味着粒子和反粒子经历了与引力场相同的耦合，包括所有相对论量子运动修正。我们的结果证明了量子力学与广义相对论的一致性，并暗示氢和反氢引力相互作用的可能差异应直接归因于“第五力”（“精髓”）。
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences ("surprises") related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously in [D.R. Brill and J.A. Wheeler, Rev. Mod. Phys., vol. 29, p. 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion the curved-space Dirac equation from East-Coast to West-Coast conventions, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes anti-particles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particles and antiparticles experience the same coupling to the gravitational field, including all relativistic quantum corrections of motion. Our results demonstrate the consistency of quantum mechanics with general relativity and imply that a conceivable difference of gravitational interaction of hydrogen and antihydrogen should directly be attributed to a a "fifth force" ("quintessence").