A note on quantization of matrix models

TL;DR

This paper explores a background independent approach to quantizing matrix models non-perturbatively, proposing a modification to the action principle that leads to algebraic relations akin to quantum theory, with potential applications to field theory.

Contribution

It introduces a natural modification to the action principle for matrix models that yields quantum algebraic relations, extending the formalism to many degrees of freedom by using a single matrix.

Findings

The modified action produces algebraic relations describing quantum theory.

A single matrix can encode all degrees of freedom for the model.

Discussion on extending the scheme to field theories and various matrix models.

Abstract

The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It is shown that this model has an ordinary mechanical system evolving in time as a classical solution. But in this treatment the action principle admits a natural modification which results in algebraic relations describing quantum theory. The origin of quantization is similar to that in Adler's generalized quantum dynamics. The problem with extension of this formalism to many degrees of freedom is solved by packing all the degrees of freedom into a single matrix. The possibility to apply this scheme to field theory and to various matrix models is discussed.