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Noncommutative differential calculus and application to gauge theory on Moyal space

Axel Marcillaud de Goursac

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Abstract

We introduce graded derivation-based differential calculus for epsilon-graded associative algebras (or color algebras). A corresponding notion of noncommutative connection is also defined. We then apply this formalism to a graded version of the Moyal algebra, for which we recover the recently constructed candidate for a renormalizable gauge action on Moyal space supplemented by terms built from a scalar field and a 2-covariant symmetric tensor field.

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What this paper is about

We introduce graded derivation-based differential calculus for epsilon-graded associative algebras (or color algebras). A corresponding notion of noncommutative connection is also defined. We then apply this formalism to a graded version of the Moyal algebra, for which we recover the recently constructed candidate for a renormalizable gauge action on Moyal space supplemented by terms built from a scalar field and a 2-covariant symmetric tensor field.

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Available abstract

We introduce graded derivation-based differential calculus for epsilon-graded associative algebras (or color algebras). A corresponding notion of noncommutative connection is also defined. We then apply this formalism to a graded version of the Moyal algebra, for which we recover the recently constructed candidate for a renormalizable gauge action on Moyal space supplemented by terms built from a scalar field and a 2-covariant symmetric tensor field.

Key concepts: Quantum differential calculus, Noncommutative geometry, Noncommutative algebraic geometry, Differential calculus, Noncommutative quantum field theory, Mathematics, Differential form, Covariant transformation

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