Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory
Pei-Ming Ho, Hsien-Chung Kao
TL;DR
This paper derives noncommutative quantum mechanics from quantum field theory, revealing charge-dependent noncommutativity and discussing implications for atomic spectra and grand unified theories.
Contribution
It introduces a method to obtain noncommutative quantum mechanics from field theory and explores charge-dependent noncommutativity effects.
Findings
Opposite charges exhibit opposite noncommutativity.
No noncommutative correction to hydrogen spectrum at tree level.
Discusses challenges and proposes a noncommutative SU(5) GUT framework.
Abstract
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously, and propose a way to construct noncommutative SU(5) grand unified theory.
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