Coupled oscillators and Feynman's three papers

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction

Possible signatures for tetraquarks from the decays of a0(980)a_0(980), a0(1450)a_0(1450)

Based on the recent proposal for the tetraquarks with the mixing scheme, we investigate fall-apart decays of $a_0(980), a_0(1450)$ into two lowest-lying mesons. This mixing scheme suggests that $a_0(980)$ and $a_0(1450)$ are the tetraquarks with the mixtures of two spin configurations of diquark and antidiquark. Due to the relative sign differences in the mixtures, the couplings of fall-apart decays into two mesons are strongly enhanced for $a_0(980)$ but suppressed for $a_0(1450)$. We report that this expectation is supported by their experimental decays. In particular, the ratios of the associated partial decay widths, which depend on some kinematical factors and the couplings, are found to be around $\Gamma [a_0(980)\rightarrow \pi \eta]/\Gamma [a_0(1450)\rightarrow \pi \eta] = 2.51-2.54$, $\Gamma [a_0(980)\rightarrow K\bar{K}]/\Gamma [a_0(1450)\rightarrow K\bar{K}] = 0.52-0.89$, which seems to agree with the experimental ratios reasonably well. This agreement can be interpreted as the tetraquark signatures for $a_0(980), a_0(1450)$.Comment: 6 pages, no figures, more references are added, the version to be published in EPJ

Group Contractions: Inonu, Wigner, and Einstein

Einstein's $E = mc^{2}$ unifies the momentum-energy relations for massive and massless particles. According to Wigner, the internal space-time symmetries of massive and massless particles are isomorphic to $O(3)$ and $E(2)$ respectively. According to Inonu and Wigner, $O(3)$ can be contracted to $E(2)$ in the large-radius limit. It is noted that the $O(3)$-like little group for massive particles can be contracted to the $E(2)$-like little group for massless particles in the limit of large momentum and/or small mass. It is thus shown that transverse rotational degrees of freedom for massive particles become contracted to gauge degrees of freedom for massless particles.Comment: 9 pages, LaTeX file, no figures; presented at the 2nd International Workshop on Classical and Quantum Integrable Systems: Algebraic Methods and Lie Algebra Contractions (Dubna, July 8-12, 1996), to be published in the Proceeding