Modern Physics Letters A

The evolution of ideas which has led from the first proofs of the renormalizability of non-Abelian gauge theories, based on Slavnov–Taylor identities, to the modern proof based on the BRS symmetry and the master equation is recalled. This lecture has been delivered at the Symposium in Honour of Professor C. N. Yang, Stony Brook, May 21, 22, 1999.

We develop a quantization condition for the excited states of simple quantum-mechanical models. The approach combines perturbation theory for the oscillatory part of the eigenfunction with a rational approximation to the logarithmic derivative of the nodeless part of it. We choose one-dimensional anharmonic oscillators as illustrative examples.

A vexing problem involving nonassociativity is resolved, allowing a generalization of the usual complex Möbius transformations to the octonions. This is accomplished by relating the octonionic Möbius transformations to the Lorentz group in ten space–time dimensions. The result will be of particular interest to physicists working with lightlike objects in ten dimensions.

We consider firstly simple D=4 superalgebra with six real tensorial central charges Z_μν, and discuss its possible realizations in massive and massless cases. Massless case is dynamically realized by generalized Ferber–Shirafuji (FS) model with fundamental bosonic spinor coordinates. The Lorentz invariance is not broken due to the realization of central charges generators in terms of bosonic spinors. The model contains four fermionic coordinates and possesses three κ-symmetries thus providing the BPS configuration preserving 3/4 of the target space supersymmetries. We show that the physical degrees of freedom (eight real bosonic and one real Grassmann variable) of our model can be described by OSp(8|1) supertwistor. The relation with recent superparticle model by Rudychev and Sezgin is pointed out. Finally we propose a higher-dimensional generalization of our model with one real fundamental bosonic spinor. D=10 model describes massless superparticle with composite tensorial central charges and in D=11 we obtain zero-superbrane model with nonvanishing mass which is generated dynamically.

The ten nonleptonic weak decays K→2π, K→ 3π, K_L→2γ, K_S→2γ, K_L→π⁰2γ, are predicted for a chiral pole model based on the linear sigma model theory which automatically satisfies the partial conservation of axial current (PCAC) hypothesis. These predictions, agreeing with data to the 5% level and containing no or at most one free parameter, are compared with the results of chiral perturbation theory (ChPT). The latter ChPT approach to one-loop level is known to contain at least four free parameters and then predicts a K_L→π⁰γγ rate which is 60% shy of the experimental value.

We have calculated the dispersion relation for the high energy cosmic rays (protons, electrons and neutrinos) propagating in the Bose gas as well as Bose condensate (BC) medium of the pseudo-scalar particles (axions and majorons). For cosmic rays propagating in the Bose gas, the mass of the particle will decrease and this is proportional to the boson density in the medium. On the other hand, the BC of the same particle will increase the mass of the fermion. If the propagating fermion is massless, it will develop an imaginary mass and thus will be absorbed in the medium. But if the condition m²/m_ϕp₀≃ 1 is satisfied, the cosmic rays will propagate freely without losing energy in the BC medium. The Bose gas and BC of the pseudo-scalar background contribution to the dispersion relation of the high energy cosmic rays is too small to have any practical importance to high energy cosmic rays physics.

The effects of matter density fluctuation in long baseline neutrino oscillation experiments are studied. Effects of short wavelength fluctuations are irrelevant. Effects of long wavelength fluctuations must be checked on a case-by-case basis. As an example we checked the fluctuation effects and showed its irrelevance in a case of K2K experiments.

Bound system composed of the Yang monopole coupled to a particle of the isospin by the SU(2) and Coulomb interaction is considered. The generalized Runge–Lenz vector and the SO(6) group of hidden symmetry are established. It is also shown that the group of hidden symmetry makes it possible to calculate the spectrum of system by a pure algebraic method.