39,437 research outputs found
Decomposition of Time-Ordered Products and Path-Ordered Exponentials
We present a decomposition formula for , an integral of time-ordered
products of operators, in terms of sums of products of the more primitive
quantities , which are the integrals of time-ordered commutators of the
same operators. The resulting factorization enables a summation over 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 . 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
Spinor Helicity Technique and String Reorganization for Multiloop Diagrams
Methods to apply the spinor helicity technique and string reorganization to
multiloop amplitudes using the Feynman- and Schwinger-parameter representations
are reviewed and expanded.Comment: 41 pages in Plain Tex, plus 6 pages of (fourteen) figures in a
postcript file attached to the end of the Tex file; McGill/93-2
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