Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity

TL;DR

This paper explores how space noncommutativity can be integrated into field theory by extending quantum mechanics, revealing that noncommutativity parameters influence free fields even without interactions.

Contribution

It introduces a method to incorporate space noncommutativity into field theory via spectral extension of quantum mechanics, including free fields.

Findings

Noncommutativity parameter affects free field behavior.

Extension of quantum mechanics to field theory with noncommutativity.

Spectral continuum approach enables noncommutative field theory formulation.

Abstract

We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In addition to the usual $\star$-product deformation of the algebra of field functions, we show that the parameter of noncommutativity can occur in noncommutative field theory even in the case of free fields without self-interacting potentials.