标题： 投影表示的非惯性对称性：量子力学中的非惯性哈密顿群的投影表示 显示英文标题

标题： Projective Representations of the Inhomogeneous Hamilton Group: Noninertial Symmetry in Quantum Mechanics

摘要： 量子力学中的对称性由李群的射影表示来实现，因为物理态仅定义到相位的相差。 一个基石定理表明这些表示等价于群的中心扩展的酉表示。 特殊相对论量子力学的惯性态作为非齐次洛伦兹群的射影表示的表述，以及其非相对论极限以伽利略群的形式，是基本的例子。 有趣的是，这两种对称性都不包括外尔-海森堡群；其代数的埃尔米特表示是海森堡对易关系，这是量子力学的基础。 外尔-海森堡群是阿贝尔群的一个一维中心扩张，因此它的酉表示是相空间平移阿贝尔群的特定射影表示。 涉及自同构群的一个定理表明，保持海森堡对易关系不变的最大对称性本质上是非齐次辛群的射影表示。 在非相对论域中，我们必须有牛顿时间的不变性。 这将对称群减少到哈密顿方程的非惯性局部对称群，即哈密顿群。 这些群的射影表示是利用麦基定理计算的，适用于非阿贝尔正规子群的一般情况。 显示英文摘要

摘要： Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary representations of the central extension of the group. The formulation of the inertial states of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group, and its nonrelativistic limit in terms of the Galilei group, are fundamental examples. Interestingly, neither of these symmetries includes the Weyl-Heisenberg group; the hermitian representations of its algebra are the Heisenberg commutation relations that are a foundation of quantum mechanics. The Weyl-Heisenberg group is a one dimensional central extension of the abelian group and its unitary representations are therefore a particular projective representation of the abelian group of translations on phase space. A theorem involving the automorphism group shows that the maximal symmetry that leaves invariant the Heisenberg commutation relations are essentially projective representations of the inhomogeneous symplectic group. In the nonrelativistic domain, we must also have invariance of Newtonian time. This reduces the symmetry group to the inhomogeneous Hamilton group that is a local noninertial symmetry of Hamilton's equations. The projective representations of these groups are calculated using the Mackey theorems for the general case of a nonabelian normal subgroup.