Feynman disentangling method and group theory

Feynman operator calculus and singular quantum oscillator

New applications of Feynman disentangling method in quantum mechanics are studied and the time-dependent singular oscillator problem is solved in this approach. The important role of representation group theory is discussed in this context.

$\left\{ h(1) \oplus h(1) \right\} \uplus u(2)$含时量子哈密顿量的时间演化算符：一种基于费曼解缠规则的自洽求解方法

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

本研究针对含$\left\{ h(1) \oplus h(1) \right\} \uplus u(2)$结构的含时量子哈密顿量，运用费曼解缠规则自洽求解时间演化算符，将问题归结为复Riccati微分方程并给出闭式解，还分析了二维各向同性量子谐振子相干态的含时演化。

Einstein, Wigner, and Feynman: From E = mc^{2} to Feynman's decoherence via Wigner's little groups

The 20th-century physics starts with Einstein and ends with Feynman. Einstein introduced the Lorentz-covariant world with E = mc^{2}. Feynman observed that fast-moving hadrons consist of partons which act incoherently with external signals. If quarks and partons are the same entities observed in different Lorentz frames, the question then is why partons are incoherent while quarks are coherent. This is the most puzzling question Feynman left for us to solve. In this report, we discuss Wigner's role in settling this question. Einstein's E = mc^{2}, which takes the form E = \sqrt{m^{2} + p^{2}},…

Lorentz Group in Feynman's World

R. P. Feynman was quite fond of inventing new physics. It is shown that some of his physical ideas can be supported by the mathematical instruments available from the Lorentz group. As a consequence, it is possible to construct a Lorentz-covariant picture of the parton model. It is shown first how the Lorentz group can be used for studying the internal space-time symmetries of relativistic particles. These symmetries are dictated by Wigner's little groups, whose transformations leave the energy-momentum four-vector of a given particle invariant. The symmetry of massive particles is like the th…

Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman

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. Couple…

Wigner's Spins, Feynman's Partons, and Their Common Ground

The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincaré group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless particle is isomorphic to the two-dimensional Euclidean group with one rotational and two translational degrees of freedom. The rotational degree corresponds to the helicity, and the translational degrees to the gauge degree of freedom. The question then is whether these two different symmetries can be united. Another hard-pressing problem is Feynman's parton p…