Space-Time Quantization and Nonlocal Field Theory —Relativistic Second Quantization of Matrix Model—

We propose relativistic second quantization of matrix model of D particles in a general framework of nonlocal field theory based on Snyder-Yang’s quantized space-time. Second-quantized nonlocal field is in general noncommutative with quantized space-time, but conjectured to become commutative with light cone time X+. This conjecture enables us to find second-quantized Hamiltonian of D particle system and Heisenberg’s equation of motion of second-quantized D field in close contact with Hamiltonian given in matrix model. We propose Hamilton’s principle of Lorentz-invariant action of D field and investigate what conditions or approximations are needed to reproduce the above Heisenberg’s equation given in light cone time. Both noncommutativities appearing in position coordinates of D particles in matrix model and in quantized space-time will be eventually unified through second quantization of matrix model. ∗ Em. Professor of Kyoto University and Associate Member of Atomic Energy Research Institute, Nihon University. E-mail: [email protected]