Galilean covariance of quantum-classical hybrid systems of the Sudarshan type

Note on Possibility of obtaining a non-relativistic proof of the spin-statistics theorem in the Galilean frame

We replay to the critique by Sudarshan and Shaji of our argument of impossibility to obtain a non-relativistic proof of the spin-statistics theorem in the Galilean frame.

Gauge transformations and Galilean covariance in nonlinear gauge-coupled quantum fluids

We investigate certain invariance properties of quantum fluids subject to a nonlinear gauge potential. In particular, we derive the covariant transformation laws for the nonlinear potentials under a space-time Galilean boost and consider U(1) gauge transformations. We find that the hydrodynamic canonical field equations are form-invariant in the case of external gauge functions, but not for nonlinear gauge functionals. Hence, nonlinear gauge potentials are non-trivial potentials which may not be "gauged-away". Notably, for a 1D superfluid, attempting to do so generates the gauge-pressure of th…

伽利略boost不变性不存活于迹：开放量子系统中的对称性破缺

Galilean boost invariance does not survive the trace: symmetry breaking in open quantum systems

研究揭示了伽利略不变性在开放量子系统中因耗散反交换项破坏，波动-耗散定理与减少的boost协变性无法共存，冷原子和超冷分子处于临界点，参数驱动抑制了boost破坏。

伽利略相对性与波粒二象性蕴含 Schrödinger 方程

Galilean relativity and wave-particle duality imply the Schrödinger equation

该研究利用 Galileo/Lorentz 协变性与 de Broglie 波粒二象性，导出 Schrödinger 方程及波函数助推变换，并在相对论情形得到 Klein–Gordon 方程与 Lorentz 协变 Schrödinger 方程。

Galilei covariance and Einstein's equivalence principle in quantum reference frames

The covariance of the Schrödinger equation under Galilei boosts and the compatibility of nonrelativistic quantum mechanics with Einstein's equivalence principle have been constrained for so long to the existence of a superselection rule which would prevent a quantum particle from being found in superposition states of different masses. In an effort to avoid this expedient, and thus allow nonrelativistic quantum mechanics to account for unstable particles, recent works have suggested that the usual Galilean transformations are inconsistent with the nonrelativistic limit implied by the Lorentz t…

代数量子动力学与SR选择

Algebraic quantum kinematics: Galilean covariance with positive energy confines unequal-time commutation to null sets

本文提出一个算子代数框架，将非相对论量子力学与狭义相对论联系起来，探讨了光子部分的实现、常数c和ħ的不同作用以及哈格-卡斯特勒网的结构障碍，提出了SR选择猜想。