The paper proves that generalized spin-boson models with normal or 2-nilpotent interactions can be ultraviolet renormalized, with norm resolvent convergence of the regularized Hamiltonians to an explicitly constructed limiting operator.
Spin-Boson Model through a Poisson-Driven Stochastic Process
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abstract
We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.
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Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions
The paper proves that generalized spin-boson models with normal or 2-nilpotent interactions can be ultraviolet renormalized, with norm resolvent convergence of the regularized Hamiltonians to an explicitly constructed limiting operator.