Clothed particle representation in quantum field theory: mass renormalization

Abstract

The method of unitary clothing transformations is used to handling the so-called clothed particle representation (CPR) (see [A.V. Shebeko and M.I. Shirokov, Phys. Part. Nucl. 32 (2001) 31; nucl-th/0102037 , V.Yu. Korda and A.V. Shebeko, Phys. Rev. D 70 (2004) 085011, V.Yu. Korda, L. Canton and A.V. Shebeko, doi:10.1016/j.aop.2006.07.010 , Ann. Phys. (2006) in press; nucl-th/060325 ] and refs. therein), where the total field Hamiltonian H and the three boost operators in the instant form of relativistic dynamics take on the same sparse structure in the Hilbert space of hadronic states. In this approach the mass counterterms are cancelled by commutators of the generators of clothing transformations and the field interaction operator. This allows the pion and nucleon mass shifts to be expressed through the corresponding three-dimensional integrals whose integrands are proved to be dependent on certain covariant combinations of the relevant three-momenta. The property provides the momentum independence of mass renormalization.