Grand Unification from Gauge Theory on M4×ZNM_4 \times Z_N

The SU(5) grand unified theory (GUT) is derived from the geometrical point of view of gauge theory on three-sheeted space-time, i.e., $M_4 \times Z_3$ manifold without recourse to noncommutative geometry. A derivation of SO(10) GUT is also discussed in the same point of view.Comment: 11 pages, 7 figures, style changed to revtex, added reference to section 1, corrected typo

PROBABILISTIC INTERPRETATION AND THE QUANTUM THEORY OF MEASUREMENT

The logical foundation of the probabilistic interpretation of quantum-mechanical states is reexamined in view of Fukuda's newtheory of measurement. We suggest that the probabilistic interpretation could be viewed as a natural consequence of thereduction of states upon measurement, rather than an a prioriansatz contained in the "external observation" framework ofquantum mechanics