标题： 非惯性系的互惠相对性：量子力学 显示英文标题

标题： Reciprocal relativity of noninertial frames: quantum mechanics

摘要： 非惯性变换在时间-位置-动量-能量空间{t,q,p,e}上被研究，其具有不变的 Born-Green 度规 ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) 和辛度规 -de/\dt +dp/\dq 。这个 U(1,3) 变换群包含洛伦兹群作为惯性特殊情况。在小力和速度极限下，它会退化为预期的哈密顿变换，保持辛度规和非相对论线元素 ds^2=dt^2 不变。U(1,3) 变换通过 c 限制相对速度，通过 b 限制相对力。时空不再是一个不变子空间，而是相对于非惯性观察者框架而言的。Born 由于位置和动量自由度之间的对偶概念而导出了该度规，因此我们称其为对偶相对论。对于大的 b，这些效应几乎肯定只会在量子领域中显现。Wigner 表明，狭义相对论量子力学来自于非齐次洛伦兹群的投影表示。李群的投影表示等价于其中心扩张的单位表示。同样的非齐次 U(1,3) 群的投影表示方法用于定义非惯性情况下的量子理论。非齐次 U(1,3) 群的中心扩张是四重群 Q(1,3)=U(1,3)*s H(4) 的覆盖。H(4) 是 Weyl-Heisenberg 群。从卡西米尔算子的表示中得出一组二阶波动方程。 显示英文摘要

摘要： Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators.