The Schrödinger equation for quantum fields with nonlinear nonlocal scattering
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This paper considers perturbationsH=H0+εV of the Hamiltonian operatorH0 of a free scalar Boson field.V is a polynomial in the annihilation creation operators. Terms of any order are allowed inV, but point interactions, such as ∫:0(x)4(x)4:dx, are not considered. Unnormalized solutions for the Schrödinger equation are found. For ε→0, these solutions have a partial asymptotic expansion in powers of ε. The set of all possible pertubation termsV forms a Lie algebra. General properties of this Lie algebra are investigated.
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Asymptotic Expansion
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