  We report the results obtained in the study of Alain Connes noncommutative
spectral geometry construction focusing on its essential ingredient of the
algebra doubling. We show that such a two-sheeted structure is related with the
gauge structure of the theory, its dissipative character and carries in itself
the seeds of quantization. From the algebraic point of view, the algebra
doubling process has the same structure of the deformed Hops algebra structure
which characterizes quantum field theory.
