Finite-dimensional approximation of the scattering matrix
A finite-dimensional nonperturbative approximation scheme of the time-evolution operator and the S matrix for relativistic field theories is discussed. It is amenable to computer calculations. Parallels with lattice-field theory are drawn. The method is outlined for the ϕ4 theory. Equivalence to standard perturbation theory in the weak-coupling regime is obtained in the limit of the approximation parameters. The method is tested numerically for nonrelativistic proton–proton s-wave scattering and the the ϕ4 model in the weak-coupling regime in 1 + 1 dimensions. In both examples, convergence to the reference solution is found.
1985 ◽
Vol 164
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pp. 117-120
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2001 ◽
2000 ◽
Vol 73
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pp. 439-456
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2020 ◽
Vol 20
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pp. 109-120
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1987 ◽
Vol 48
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pp. 565-565
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1992 ◽
Vol 114
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pp. 580-587
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2000 ◽
Vol 6
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pp. 79-91
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