Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$. Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
弦模型被设计用来提供相对论粒子内部时空结构的协变描述。绳子是一系列像珍珠项链一样的巨大珠子的限制情况。在无限个零质量小球的极限下，它成为场论弦。另一个有趣的限制是通过消除所有其他珍珠来只保留两个珍珠，从而产生谐振子。振荡器模型的基本优点是数学上的简单。这鼓励我们为相对论扩展粒子的协变图像构造双珍珠弦。我们通过变换Feynman { \it et al.}转化为庞加莱群的表示然后，我们为这些振子态构造了类O（3）小群的表示，这决定了它们内部的时空对称性。这个简单的数学过程使我们能够用基本的时空对称性来解释我们在世界上观察到的东西，模型的内在协方差使我们能够用静止框架中的物理来解释无限动量框架中发生的事情。这样就有可能用静止坐标系中的夸克波函数来计算以光速运动的质子内部的部分子分布。
Towards quantum computing Feynman diagrams in hybrid qubit-oscillator devices
Instituto de Física Teorica, UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Department of Physics, University of Oxford（牛津大学物理系）；Department of Physics, Swansea University（斯旺西大学物理系）
Feynman-Vernon model of a moving thermal environment
本文回顾了标准布朗粒子在外势$V(x,t)$中运动的线性耗散系统的Feynman-Vernon模型，介绍了布朗粒子与热环境耦合的广义振子模型$v_{env}$ .运动环境中的扩散过程是人们感兴趣的，例如在研究超流体中的涡旋运动时。本文的出发点是考虑热环境的空间和时间不变性的振子模型的公式化[M。Patriarca，Statistical correlations in the oscillator model of quantum布朗运动，Il Nuovo Cimento B，111（1），61-72（1996），doi：10.1007/BF 02726201，arXiv：1801.02429]，它具有有限的性质并且与经典极限一致。导出了运动环境中布朗粒子的朗之万方程和影响泛函。
Time evolution operator for a $\left\{ h(1) \oplus h(1) \right\} \uplus u(2)$ time-dependent quantum Hamiltonian; a self-consistent resolution method based on Feynman's disentangling rules
