Decomposition of Time-Ordered Products and Path-Ordered Exponentials

We present a decomposition formula for $U_n$, an integral of time-ordered products of operators, in terms of sums of products of the more primitive quantities $C_m$, which are the integrals of time-ordered commutators of the same operators. The resulting factorization enables a summation over $n$ to be carried out to yield an explicit expression for the time-ordered exponential, an expression which turns out to be an exponential function of $C_m$. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.Comment: 31 pages, Revtex with two postscript figure

Mass Independent Textures and Symmetry

A mass-independent texture is a set of linear relations of the fermion mass-matrix elements which imposes no constraint on the fermionic masses nor the Majorana phases. Magic and 2-3 symmetries are examples. We discuss the general construction and the properties of these textures, as well as their relation to the quark and neutrino mixing matrices. Such a texture may be regarded as a symmetry, whose unitary generators of the symmetry group can be explicitly constructed. In particular, the symmetries connected with the tri-bimaximal neutrino mixing matrix are discussed, together with the physical consequence of breaking one symmetry but preserving another.Comment: Version to be published in PRD. References modified, and a misprint in eq (9) is correcte

Probing Extra Dimensions with Neutrino Oscillations

In the braneworld scenario, gravity and neutrino oscillation can both be used to detect the presence of an extra dimension. We argue that neutrino oscillation is particularly suitable if the size of the extra dimension is small, in which case the signature for the extra dimension is the disappearance of active neutrino fluxes into the bulk, caused by the destructive interference from the Kaluza-Klein states. We discuss a class of models to illustrate this general feature.Comment: 16 pages, no figures. A contribution in honor of Hiroshi Ezawa on his 70th birthday. To appear in `Garden of Quanta' (World Scientific