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

Abstract

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 {\bf D} field in close contact with Hamiltonian given in matrix model. We propose Hamilton's principle of Lorentz-invariant action of {\bf 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.

22 pages, no figures (plain TeX with PHYZZX macro), Eq.(4.3) corrected, Eq. (5.6) corrected, minor changes of expression in section 5, a footnote on Eq.(5.6) and one reference added

References in corpus (1)

• Towards Covariant Matrix Theory

Cited by in corpus (5)

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• Where Does Black Hole Entropy Lie? Some Remarks on Area-Entropy Law, Holographic Principle and Noncommutative Space-Time
• Kinematical Holographic Relation in Yang's Quantized Space-Time and Area-Entropy Relation in $D_0$ Brane Gas System