Noncommutative Geometry and Gauge Theory on Fuzzy Sphere
Ursula Carow-Watamura, Satoshi Watamura (Tohoku Univ.)
TL;DR
This paper constructs a differential algebra on the fuzzy sphere using Connes' scheme, defines a U(1) gauge theory, and explores gauge transformations and scalar field interactions within this noncommutative geometric framework.
Contribution
It introduces a new differential algebra on the fuzzy sphere and formulates a U(1) gauge theory with explicit gauge transformations and scalar field interactions.
Findings
Defined the differential algebra on the fuzzy sphere.
Established the U(1) gauge theory and local gauge transformations.
Described the interaction with a complex scalar field.
Abstract
The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is identified with the left transformation of the field, where a field is a bimodule over the quantized algebra . The interaction with a complex scalar field is also given.
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