Renormalization for free harmonic oscillators
Abstract
We introduce a model of free harmonic oscillators that requires renormalization. The model is similar to but simpler than the soluble Lee model. We introduce two concrete examples: the first, resembling the three dimensional φ4 theory, needs only mass renormalization, and the second, resembling the four dimensional φ4 theory and the Lee model, needs additional renormalization of a coupling and a wave function.
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