Using the partially conserved axial-vector current and the commutation relations of the vector an... more Using the partially conserved axial-vector current and the commutation relations of the vector and axial-vector currents with themselves and with the Hamiltonian responsible for weak nonleptionic decays, we demonstrate how to expand weak-decay amplitudes in the momenta of pions involved in the decays. The resulting expansion gives the on-mass-shell decay amplitude up to first order in pion momenta. We apply these techniques to the three-pion decays of kaons and show that they quantitatively reproduce the experimental situation of an amplitude linearly dependent on the "odd"-pion kinetic energy. All three pions are treated on an equal footing, and on-the-mass-shell quantities are dealt with everywhere.
Lyapunov exponents from observed time series. Paul Bryant and Reggie Brown Institute for Nonlinea... more Lyapunov exponents from observed time series. Paul Bryant and Reggie Brown Institute for Nonlinear Science, University of California at San Diego, La Jolla, California 92093-0402. Henry DI Abarbanel Department of Physics ...
We examine the issue of determining an acceptable minimum embedding dimension by looking at the b... more We examine the issue of determining an acceptable minimum embedding dimension by looking at the behavior of near neighbors under changes in the embedding dimension from d→d+1. When the number of nearest neighbors arising through projection is zero in dimension d ...
Using the partially conserved axial-vector current and the commutation relations of the vector an... more Using the partially conserved axial-vector current and the commutation relations of the vector and axial-vector currents with themselves and with the Hamiltonian responsible for weak nonleptionic decays, we demonstrate how to expand weak-decay amplitudes in the momenta of pions involved in the decays. The resulting expansion gives the on-mass-shell decay amplitude up to first order in pion momenta. We apply these techniques to the three-pion decays of kaons and show that they quantitatively reproduce the experimental situation of an amplitude linearly dependent on the "odd"-pion kinetic energy. All three pions are treated on an equal footing, and on-the-mass-shell quantities are dealt with everywhere.
Lyapunov exponents from observed time series. Paul Bryant and Reggie Brown Institute for Nonlinea... more Lyapunov exponents from observed time series. Paul Bryant and Reggie Brown Institute for Nonlinear Science, University of California at San Diego, La Jolla, California 92093-0402. Henry DI Abarbanel Department of Physics ...
We examine the issue of determining an acceptable minimum embedding dimension by looking at the b... more We examine the issue of determining an acceptable minimum embedding dimension by looking at the behavior of near neighbors under changes in the embedding dimension from d→d+1. When the number of nearest neighbors arising through projection is zero in dimension d ...
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