Springer Online Journal Archives 1860-2000
Abstract The (non-Lorentz covariant) system consisting of a relativistic scalar Boson field ϕ interacting with a single spinless particle (relativistic polaron) with kinetic energy function (m 2+|p|2)1/2 is studied ind space demensions, whered≧3. The interaction Hamiltonian is taken to be ∝ Ψ (x)* Ψ(x) ϕ(x)dx where ϕ has a momentum cutoff. The physical one polaron Hilbert space ℋ ph for this model, corresponding to no cutoff on ϕ, is constructed. The total renormalized HamiltonianH without cutoff is constructed as a semibounded self-adjoint operator on ℋ pH . The time zero physical Boson field is also constructed. First order estimates are established for the local (in momentum space) number operators in terms ofH.
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