Gauge theories with graded differential Lie algebras
Raimar Wulkenhaar
TL;DR
This paper introduces a new mathematical framework for gauge theories using graded differential Lie algebras, skew-adjoint Lie algebras, and generalized Dirac operators on Hilbert spaces.
Contribution
It develops a novel formalism combining graded differential Lie algebras with gauge theories, expanding the mathematical tools available for their analysis.
Findings
Provides a rigorous mathematical structure for gauge theories
Integrates generalized Dirac operators into the gauge theory framework
Lays groundwork for future theoretical developments in gauge symmetries
Abstract
We present a mathematical framework of gauge theories that is based upon a skew-adjoint Lie algebra and a generalized Dirac operator, both acting on a Hilbert space.
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