2025/10/07 by V. I. Lapushkin, Lapushkin, V. I.
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2510.06129
openalex publication_date 2025/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study different properties of the motion equations of interacting fields. In the second section, we prove that "Wightman's" fields (we use only a subset of Wightman's axioms) are unitarily equivalent to some operators on the vector space \cal F (with one mathematical assumption). In the third section, we introduce L∞ and DL Hilbert spaces, which are convenient for analyzing field equations, particularly the equations for ϕ3 theory. Remarkably, we have managed to reduce the equation of motion for ϕ3 to a quadratic matrix equation with matrices over a separable Hilbert space in the fourth section. Also, in the appendix, we have done the same for QCD. Furthermore, we prove the existence of solution to the motion equations of one toy model non-renormalizable theory in the fifth section.