Electric-Magnetic duality and the "Loop Representation" in Abelian Gauge Theories
Lorenzo Leal ( Universidad Central de Venezuela )
TL;DR
This paper explores a geometric quantization of Abelian Gauge Theories using a Loop Representation that symmetrically treats electric and magnetic operators, revealing a topological algebra structure.
Contribution
It introduces a generalized Loop Representation that unifies electric and magnetic operators, providing a comprehensive topological algebra framework for Abelian Gauge Theories.
Findings
Electric and magnetic operators are treated on equal footing.
The algebra of operators is topological and resembles 't Hooft's order-disorder algebra.
The approach offers a complete description of the physical phase space.
Abstract
Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of non local operators that resembles the order-disorder dual algebra of 't Hooft. These dual operators provide a complete description of the physical phase space of the theories.
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