伽利略单粒子动力学从平滑参考态家族
Galilean One-Particle Kinematics from a Smooth Family of Reference States
AI总结：
本文通过平滑参考态家族构建伽利略单粒子动力学，利用可观测量-生成量对应关系和局部惯性组合，得出不可约表示的等价性及自旋覆盖作用与中心提升-平移扭量。
摘要：
Giannelli和Chiribella从信息非平衡碰撞模型推导出能量的可观测量-生成量对偶性。本文研究旨在伽利略单粒子领域的连续变量版本。围绕各向同性平衡的平滑参考态家族提供时间、平移、旋转和提升方向。通过微分平滑扩展的单态对偶映射获得局部可观测量-生成量对应关系，利用fiducial聚焦假设与协变性获得局部定位的规范一性。结合标准的协变局部化可观测量模糊形式，得到精确的局部化。通过局部惯性组合、旋转的自旋覆盖作用和中心提升-平移扭量，每个不可约表示都与Hilbert空间L2(R3)张量(2s+1)维自旋空间等价。在该表示中，平移由规范动量生成，扭量是标量质量m>0，t=0时的提升由m倍位置可观测量生成，哈密顿量是自由粒子动能加常数E0，总角动量是轨道加自旋。
英文摘要：
Giannelli and Chiribella derived an observable-generator duality for energy from a collision model of informational nonequilibrium. We study a continuous-variable version aimed at the Galilean one-particle sector. A smooth family of reference states around an isotropic equilibrium supplies time, translation, rotation, and boost directions. The local observable-generator correspondence is obtained by differentiating a smooth extension of the single-state duality map, and the norm-one property of localization is obtained from a fiducial focusing assumption together with covariance. Combined with the standard smearing form of covariant localization observables, this yields sharp localization. With local inertial composition, the spin-cover action of rotations, and a central boost-translation holonomy, every irreducible sector is unitarily equivalent to the Hilbert space L2(R3) tensored with a (2s+1)-dimensional spin space. In that representation translations are generated by the canonical momentum, the holonomy is a scalar mass m > 0, boosts at t = 0 are generated by m times the position observable, the Hamiltonian is the free-particle kinetic term plus a constant E0, and the total angular momentum is orbital plus spin.
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