Quadratic Fermion Interaction Hamiltonian

Abstract

The interaction Hamiltonian λ ∫ :(0)(x)ψ(0)(x):g(x)dsx,g(x) ∊ S(Rs)λ∫:ψ̄(0)(x)ψ(0)(x):g(x)dsx,g(x)∊S(Rs) is studied. An ultraviolet cutoff is introduced. We remove this cutoff, and take the limit g → 1 in S(Rs)S(Rs), by working with the Heisenberg fields. The limiting fields are well defined on the Fock space associated with the bare mass m0. In the limit we get a new representation of the canonical anticommutation relations which is given by a (generalized) Bogoliubov transformation. The new representation is not always unitarily equivalent to the bare mass Fock representations.