Three Body Bound State in Non-Commutative Space

TL;DR

This paper derives a Schrödinger equation for a three-body bound state in non-commutative space from the Bethe-Salpeter equation in NCQED, and uses Helium data to constrain the non-commutativity parameter.

Contribution

It introduces a non-commutative space formulation for three-body bound states and establishes experimental bounds on non-commutativity from atomic data.

Findings

Upper bound on non-commutativity parameter $ heta$ from Helium data

Derivation of Schrödinger equation in non-commutative space for three-body systems

Connection between non-commutative quantum field theory and atomic physics

Abstract

The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schr\"{o}dinger equation in non-commutative space. It is shown that the experimental data for Helium atom puts an upper bound on the magnitude of the parameter of non-commutativity, $\theta\sim10^{-9}\lambda_e^2$.