Noncommutative scalar fields from symplectic deformation

TL;DR

This paper explores the quantum theory of noncommutative scalar fields in two dimensions, showing how symplectic deformation leads to noncommutativity, and analyzes the resulting effects on field quantization and energy degeneracies.

Contribution

It introduces a novel approach to noncommutative scalar fields via symplectic deformation and derives the quantization and mode expansions in an electromagnetic background.

Findings

Noncommutativity arises from symplectic structure deformation.

Quantization and mode expansions are explicitly derived.

Deformation lifts degeneracies in the Hamiltonian.

Abstract

This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space time. It is shown that the noncommutativity originates from the the deformation of symplectic structures. The quantization is performed and the modes expansions of the fields, in presence of an electro-magnetic background, are derived. The Hamiltonian of the theory is given and the degeneracies lifting, induced by the deformation, is also discussed.