Space-Time Quantization and Matrix Model

In order to get the general framework describing a nonlocalizable object beyond the bilocal field theory early proposed by Markov and Yukawa, the quantization of space-time is reconsidered and further developed. Space-time quantities are there not only noncommutative with U -field describing the nonlocalizable object, as in the bilocal field theory, but also become noncommutative among themselves. Under the U -field representation, where the basis vectors of representation are chosen to be eigenvectors of operator U , space-time quantities get a matrix representation of infinite dimension in general. Field equation is considered, which determines the relation between space-time quantities and U -field. The possible inner relation between the recent topics of matrix model in superstring theory and the present approach is discussed. PACS 12.90 Miscellaneous theoretical ideas and models. ∗ Em. Professor of Kyoto University and Associate Member of Atomic Energy Research Institute, Nihon University.