Abstract
In this paper, we start the investigation of a new natural approach to “unifying” noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional ([Formula: see text]) [Formula: see text]-algebras. The defining inductive sequence of an [Formula: see text] [Formula: see text]-algebra is lifted to enable the construction of a sequence of NCGFT of Yang–Mills–Higgs types. This paper focuses on derivation-based noncommutative field theories. A mathematical study of the ingredients involved in the construction of a NCGFT is given in the framework of [Formula: see text] [Formula: see text]-algebras: derivation-based differential calculus, modules, connections, metrics and Hodge *-operators, and Lagrangians. Some physical applications concerning mass spectra generated by Spontaneous Symmetry Breaking Mechanisms (SSBM) are proposed using numerical computations for specific situations.
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