WSIG-QFT: Axioms, Theorems and Proofs\\ for Windowed Scattering and Information Geometry\\ in Quantum Field Theory
WSIG-QFT: Axioms, Theorems and Proofs\\ for Windowed Scattering and Information Geometry\\ in Quantum Field Theory
This paper constructs and rigorizes WSIG-QFT (Windowed Scattering \& Information-Geometry Quantum Field Theory): under weighted Mellin--logarithmic model and de Branges--Kreĭn (DBK) canonical system, uses Weyl--Heisenberg kinematic scale for ``phase--scale'', connects scattering phase derivative with (relative) spectral density via Birman--Kreĭn (BK)--Wigner--Smith (WS) chain, realizes Born probability = relative entropy minimization through Csiszár-type I-projection, implements pointer basis = spectral minimum of readout quadratic form via Ky-Fan spectral minimum, provides non-asymptotic error closure and bandlimited-sampling criterion through Nyquist--Poisson--Euler--Maclaurin (NPE). For multi-channel establishes windowed BK identity and multi-window frame--Wexler--Raz synergy conditions, giving verifiable premises, explicit statements and complete proofs (based on recognized criteria). Keywords: Windowed readout; de Branges--Kreĭn canonical system; Weyl--Heisenberg representation; Birman--Kreĭn; Wigner--Smith delay; I-projection; Wexler--Raz; Nyquist--Poisson--Euler--Maclaurin (NPE) error closure MSC: 81Txx; 47Bxx; 46E22; 42C15
- National University of Singapore Singapore
General Relativity, Modular Flow, Unified Time Scale, Information Theory, Boundary Time Geometry, Wigner-Smith Time Delay, Causal Structure, QNEC, Quantum Scattering, Generalized Entropy, Spectral Shift Function, Time Geometry
General Relativity, Modular Flow, Unified Time Scale, Information Theory, Boundary Time Geometry, Wigner-Smith Time Delay, Causal Structure, QNEC, Quantum Scattering, Generalized Entropy, Spectral Shift Function, Time Geometry
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