Noncommutative Quantum Field Theory: A Confrontation of Symmetries

The concept of a noncommutative field is formulated based on the interplay between twisted Poincar\'e symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting this construction, such as the light-wedge causality condition and the integrability condition for Tomonaga-Schwinger equation, are presented. Based on this analysis, the claim of the identity between commutative QFT and noncommutative QFT with twisted Poincar\'e symmetry is refuted.Comment: 20 page

A simulation of high energy cosmic ray propagation 1

High energy cosmic ray propagation of the energy region 10 to the 14.5 power - 10 to the 18th power eV is simulated in the inter steller circumstances. In conclusion, the diffusion process by turbulent magnetic fields is classified into several regions by ratio of the gyro-radius and the scale of turbulence. When the ratio becomes larger then 10 to the minus 0.5 power, the analysis with the assumption of point scattering can be applied with the mean free path E sup 2. However, when the ratio is smaller than 10 to the minus 0.5 power, we need a more complicated analysis or simulation. Assuming the turbulence scale of magnetic fields of the Galaxy is 10-30pc and the mean magnetic field strength is 3 micro gauss, the energy of cosmic ray with that gyro-radius is about 10 to the 16.5 power eV

Renormalization Constant of the Color Gauge Field as a Probe of Confinement

The mechanism of color confinement as a consequence of an unbroken non-abelian gauge symmetry and asymptotic freedom is elucidated and compared with that of other models based on an analogy with the type II superconductor. It is demonstrated that a sufficient condition for color confinement is given by $Z_3^{-1}=0$ where $Z_3$ denotes the renormalization constant of the color gauge field. It is shown that this condition is actually satisfied in quantum chromodynamics and that some of the characteristic features of other models follow from it.Comment: 34 pages, Latex, v2 - 2 appendices adde