On the Meaning of the String-Inspired Noncommutativity and its Implications

TL;DR

This paper offers a new interpretation of string-inspired noncommutativity, suggesting it applies only to particle coordinates, and explores its implications for quantum mechanics and field theories.

Contribution

It introduces a novel perspective on noncommutativity in string-inspired theories, focusing on particle coordinates rather than spacetime, and develops a formal structure for noncommutative quantum mechanics.

Findings

Noncommutativity should be assumed only between particle coordinates.

A consistent interpretation of the wavefunction in noncommutative quantum mechanics.

Conditions for classical and commutative limits are established.

Abstract

We propose an alternative interpretation for the meaning of noncommutativity of the string-inspired field theories and quantum mechanics. Arguments are presented to show that the noncommutativity generated in the stringy context should be assumed to be only between the particle coordinate observables, and not of the spacetime coordinates. Some implications of this fact for noncomutative field theories and quantum mechanics are discussed. In particular, a consistent interpretation is given for the wavefunction in quantum mechanics. An analysis of the noncommutative theories in the Schr\"odinger formulation is performed employing a generalized quantum Hamilton-Jacobi formalism. A formal structure for noncommutative quantum mechanics, richer than the one of noncommutative quantum field theory, comes out. Conditions for the classical and commutative limits of these theories have also been determined and applied in some examples.