FRACTIONAL DIRAC OPERATORS AND LEFT-RIGHT FRACTIONAL CHAMSEDDINE-CONNES SPECTRAL BOSONIC ACTION PRINCIPLE IN NONCOMMUTATIVE GEOMETRY

摘要

The generalization of the Chamseddine-Connes spectral triples action to its ( left and right) fractional counterpart is constructed within the context of the Riemann-Liouville and Erdelyi-Kober ( left and right) fractional operators. In the fractional approach, the Dirac operators (sic) is approximated by (sic) ((alpha))((a,-)) + (sic) ((alpha))((b,+)) for all t is an element of [a, b] and the spectral triple (C-infinity(M), L-2(M, S), (sic)) is replaced by its fractional equivalent (C-infinity(M), L-2(M, S), (sic) ((2 alpha))((a,-)) + (C-infinity(M), L-2(M, S), (sic)((b,+))((2 alpha)) , 0 < alpha < 1. When the ( left) fractional action is applied to the noncommutative space defined by the spectrum of the Standard Model, one obtains many attractive characteristics including time-dependent gauge couplings constants (g(1)(2), g(2)(2), g(3)(2)), a time-dependent cosmological constant (Lambda(cos)), a time-dependent scalar Ricci curvature (R), a time-dependent Newton's coupling constant, and a time-dependent Higgs square mass m(H1)(2). Furthermore, (g(1)(2), g(2)(2), g(3)(2)), Lambda(cos), R, and m(H1)(2) were found to be nonsingulars at the Planck's time. When the (left and right) fractional bosonic action is taken into account, all the previous functions are found to be complexified, including gravity. Many additional interesting features are discussed and explored in some details.