A Generalized Scaling Limit and its Application to the Semi-Relativistic Particles System Coupled to a Bose Field with Removing Ultraviolet Cutoffs

Details A Generalized Scaling Limit and its Application to the Semi-Relativistic Particles System Coupled to a Bose Field with Removing Ultraviolet Cutoffs A Generalized Scaling Limit and its Application to the Semi-Relativistic Particles System Coupled to a Bose Field with Removing Ultraviolet Cutoffs

2010-05-10

arxiv.org/abs/1005.1447v1

Mathematics

Functional Analysis

Scientific paper

The system of semi-relativistic particles coupled to a scalar bose field is investigated. A renormalized Hamiltonian is defined by subtracting a divergent term from the total Hamiltonian. We consider taking the scaling limit and removing the ultraviolet cutoffs simultaneously for the renormalized Hamiltonian. By applying an abstract scaling limit theory on self-adjoint operators, we derive the Yukawa potential as an effective potential of semi-relativistic particles.

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