Boson fields with bounded interaction densities
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Abstract
We consider interaction densities of the formV(φ(x)), where φ(x) is a scalar boson field andV(α) is a bounded real continuous function. We define the cut-off interaction by\(V_{\varepsilon ,r} = \int\limits_{\left| x \right|< r} {V(\phi _E (x))} \), where φE(x) is the momentum cut-off field. We prove that the scattering operator Sεr(V) corresponding to the cut-off interaction exists, and we study the behavior of the scattering operator as well as the Heisenberg picture fields, as the cut-off is removed.
Keywords
Neural Network Statistical Physic Continuous Function Complex System Nonlinear Dynamics
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References
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