Acyclic finite quantum systems make the Born-Neumann series collapse to an exact finite sum via nilpotency of T = G0(E)V, giving closed-form amplitudes such as A4 = t42 t21 + t43 t31 for diamond graphs where first-order Born fails.
Moya, Operational integration of โซ ๐ฅ๐๐๐๐ฅ ๐๐ฅ: nilpotency, finite Neumann series and algebraic reduction of integration by parts, Zenodo
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Exact Nilpotent Collapse of Born-Neumann Expansions in Finite Quantum Systems: A SON Formulation for Exact Algebraic Closures of Scattering Series
Acyclic finite quantum systems make the Born-Neumann series collapse to an exact finite sum via nilpotency of T = G0(E)V, giving closed-form amplitudes such as A4 = t42 t21 + t43 t31 for diamond graphs where first-order Born fails.