Quantum gauge symmetries in Noncommutative Geometry

摘要: We discuss generalizations of the notion i) group unitary elements a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in framework compact quantum theory spectral triples. The analogue these groups are defined as universal (initial) objects some natural categories. After proving existence objects, we several examples that interest to physics, they appear noncommutative geometry approach particle physics: particular, C*-algebras M_n(R), M_n(C) M_n(H), describing space Einstein-Yang-Mills systems, algebras A_F=C+H+M_3(C) A^{ev}=H+H+M_4(C), Chamseddine-Connes derivation Standard Model physics minimally coupled gravity. As byproduct, identify "free" version symplectic Sp(n) (quaternionic group).