Methods for the Nonperturbative Approximation of Form Factors and Scattering Amplitudes

Methods are described for the nonperturbative calculation of wave functions and scattering amplitudes in light-cone quantization. Form factors are computed from the boost-invariant wave functions, which appear as coefficients in a Fock-state expansion of the field-theoretic eigenstate. A technique is proposed for calculating scattering amplitudes from matrix elements of a T operator between such compositeparticle eigenstates. INTRODUCTION To benefit from the recent progress on the calculation of field-theoretic bound states in light-cone quantization [1,2], we explore methods by which form factors and scattering amplitudes can be extracted nonperturbatively. In the case of form factors, this is relatively straightforward; well-known formulas [3] yield the form factors as overlap integrals of Fock-state wave functions. For scattering amplitudes, the way is less certain. One possible method [4] is discussed briefly here. Others have been considered by Kröger [5], Ji and Surya [6], and Fuda [7]. The formulations given are in terms of light-cone coordinates [8,1], where x ≡ t+ z plays the role of time and the conjugate variable p ≡ E−pz is the light-cone energy. The light-cone three-momentum is p = (p ≡ E + pz,p⊥). An eigenstate |P, σ〉 of the light-cone Hamiltonian operators P±, P⊥ and helicity σ is written as a Fock-state expansion |P, σ〉 = ∑