Connection between Particle Models and Field Theories, I: The Case Spin 1/2

If we neglect, in Feynman-Dyson's rule of calculation, the contributions due to all closed loops of fermion line, we may deal with the one-particle theory for the fermion. The transformation found by Pryce, by Foldy and Wouthuysen and also independently by the author enables us to get some intuitive explanation of fermions's behavior when it is free. In this paper we will show that also when the fermions are interacting with other fields, this transformation is rather suitable to get a physical interpretation of the results. For example, we are able to compute the effects of the Zitterbewegung. Although it is profitable to work in the one-particle theory, we must interpret the negative energy states in accordance with the positron theory. So we will discuss how far we should modify the one-particle theory in order to maintain the straight parallelism to the quantized field theory. A remark is added concerning with the interpretation of charge operators, i.e., Dirac operators ρ's. Several results of the transformation are tabulated for the sake of reference in future.