We study in detail the quantum field theory of mixing among three generations of Dirac fermions (neutrinos). We construct the Hilbert space for the flavor fields and determine the generators of the mixing transformations. By use of these generators, we recover all the known parametrizations of the three flavor mixing matrix and we find a number of new ones. The algebra of the currents associated with the mixing transformations is shown to be a deformed $\mathrm{su}\left(3\right)\mathrm{}$ algebra, when $\mathrm{CP}$ violating phases are present. We then derive the exact oscillation formulas, exhibiting new features with respect to the usual ones. $\mathrm{CP}$ and T violation are also discussed.

• Received 1 May 2002

DOI:https://doi.org/10.1103/PhysRevD.66.025033