By S. Ketov

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After constructing the interaction operators in the CPR we express the conventional S matrix through the clothed-particle interactions and states that simplifies the initial field-theoretical task. It becomes possible owing to the isomorphism between the α-algebra with the bare vacuum and the αc -algebra with the physical vacuum when, first, the requirement iii) is fulfilled and, second, the R - generators of unitary clothing transformations in the Dirac picture come to zero in the distant past and future (see our talk in Durham (Shebeko, 2004)).

We define our basis space with total longitudinal momentum K=80 which we found adequate for the present application but will be extended in the future. In fact, the results presented in Ref. (10) already extend the basis to K=160. 4MeV. 511 MeV, the only scale-setting parameter in the QED Hamiltonian. At each ω we calculate ae with Nmax in the range of 10 to 118 to map out its convergence behavior with increasing Nmax . Larger Nmax translates to a larger basis with higher effective ultraviolet cutoff and lower effective infrared cutoff in the transverse plane.

It allows us to retain the GI in the course of inevitably approximate calculations. 5 6 In Eqs. (140) ηc is the projection operator on the subspace H2N ∈ H spanned on the two-clothed-nucleon states |2N = bc† bc† |Ω Of course, all nucleon polarization labels are implied here together with necessary summations over them in Eq. (141) and so on 28 26 Advances in Quantum Field Theory Will-be-set-by-IN-TECH 5. Summary We propose a constructive way of ensuring the RI in QFT with cutoffs in momentum space.

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Advances in Quantum Field Theory by S. Ketov

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