Hamiltonians without ultraviolet divergence for quantum field theories

  title={Hamiltonians without ultraviolet divergence for quantum field theories},
  author={Stefan Teufel and Roderich Tumulka},
  journal={Quantum Studies: Mathematics and Foundations},
We propose a way of defining Hamiltonians for quantum field theories without any renormalization procedure. The resulting Hamiltonians, called IBC Hamiltonians, are mathematically well defined (and in particular, ultraviolet finite) without an ultraviolet cutoff such as smearing out the particles over a nonzero radius; rather, the particles are assigned radius zero. These Hamiltonians agree with those obtained through renormalization whenever both are known to exist. We describe explicit… 
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