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THE SECOND ORDER AMPLITUDES 141
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agreement with experiment algebraic model amplitude to second Appendix assumptions axial currents calculate charge conjugation complete second order coupling constant coupling theory CR's crossing symmetry current algebra derive diagonalized Dirac equation discussion equal-time commutation expansion parameters experimental estimates form factors Gell-Mann give H.J. Schnitzer hard-pion I.S. Gerstein implies invariant amplitudes isospin-even amplitudes isospin-odd amplitudes lengths and s-wave low energy LSZ formalism Mandelstam variables mass shell mass-shell matrix elements meson n-point functions nonpole contributions nucleon contribution nucleon field nucleon pole numerical evaluation obtained on-mass-shell p-wave scattering lengths parameterized terms PCAC Phys pion four-momenta pion momenta quantities Raman s-and p-wave S-matrix s-wave effective ranges Scattering Parameters Schwinger terms second order amplitudes second order expansion soft-pion approximation soft-pion result spectral functions sum rule t-channel exchange term in Eq thesis TTN scattering amplitude vacuum expectation values vertex functions Ward-identity techniques weak amplitude Weinberg