Quantum field theory without infinities

In relativistic quantum field theories, the traditional renormalization app roach leads to Hamiltonians with infinite counterterms. The infinities canc el when this Hamiltonian is used to calculate the renormalized finite S-mat rix and related observable properties in a good agreement with experiment, However, time evolution of state vectors and observables cannot be studied without a well-defined finite Hamiltonian. Based on the "clothed particle" approach (O. W. Greenberg and S. S. Schweber, 1958, Nuovo Cimento 8, 378). we reformulate the theory in such a way that ultraviolet infinities appear neither in the S-matrix nor in the Hamiltonian. In this formulation the Ham iltonian is finite and allows us to calculate the time evolution of wave fu nctions. the S-matrix, and other properties by a straightforward applicatio n of quantum mechanical rules without renormalization. A rigorous approach to the bound states in quantum field theory is also discussed using the hyd rogen atom as an example. (C) 2001 Academic Press.