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

TL;DR

This paper develops a relativistic second quantization framework for matrix models of D particles within nonlocal, noncommutative field theory based on quantized space-time, aiming to unify noncommutativities in position and space-time.

Contribution

It introduces a novel second-quantized nonlocal field theory for matrix models, connecting noncommutative space-time with light cone time and deriving Hamiltonian dynamics.

Findings

Derived second-quantized Hamiltonian for D particles

Proposed Lorentz-invariant action principle for D field

Explored conditions for recovering matrix model equations

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.