Chiral spinors and gauge fields in noncommutative curved space-time

Abstract

The fundamental concepts of Riemannian geometry, such as differential forms, vielbein, metric, connection, torsion and curvature, are generalized in the context of non-commutative geometry. This allows us to construct the Einstein-Hilbert-Cartan terms, in addition to the bosonic and fermionic ones in the Lagrangian of an action functional on non-commutative spaces. As an example, and also as a prelude to the Standard Model that includes gravitational interactions, we present a model of chiral spinor fields on a curved two-sheeted space-time with two distinct abelian gauge fields. In this model, the full spectrum of the generalized metric consists of pairs of tensor, vector and scalar fields. They are coupled to the chiral fermions and the gauge fields leading to possible parity violation effects triggered by gravity.

50 pages LaTeX, minor corrections and references added

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Cited by in corpus (14)

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• Noncommutative gravity: fuzzy sphere and others
• Quantum dynamics of massive particles in a non-commutative two-sheeted space-time
• Noncommutative Particles in Curved Spaces
• Thermofield dynamics and Gravity
• A metric theory of gravity with torsion in extra-dimension
• Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory
• Kaluza-Klein Theory with Torsion confined to the Extra-dimension
• Exciton swapping in a twisted graphene bilayer as a solid-state realization of a two-brane model
• Noncommutative Nonlinear Supersymmetry
• The Higgs Sector on a Two-Sheeted Space Time
• Quantum dynamics of particles in a discrete two-branes world model: Can matter particles exchange occur between branes?
• Massive photon and fermion mixing as manifestations of an extra discrete dimension in bilayer systems