A New Interpretation of the Negative Energy Bose Field

Abstract

The well-known difficulties inherent in the negative energy Bose fields limit the unambiguous application of such fields in the ,ordinary quantum field theory. A correct incorporation of the negative energy Bose fields into the ordinary theory of the positive energy Bose fields, however, seems to give a promising method in order to solve the convergence difticulties of the quantum field theory. For examples, in Bopp's field(l) or Pauli's regulator methodj(2) it seems to be an essential point of the theory that the negative energy fields or the fields having the imaginary constants of coupling with the real fields are mixed with the positive energy fields. As stated by' Pauli, the current mixed theory of ordinary fields may stand on the realistic point of view, on the other hand his regulator method may stand on the formalistic point of view. Although the regulator method could be considered to be a generalized mixed field theory as mentioned above, it will be necessary that such fictitious fields have to be eliminated by some limiting procedures in the final results which make them to be only formal auxiliary fields and to have no correspondece to any observable one. The introduction of a new hypothesis into the fictitious fields, however, will allow us to infer that it would be possible to bring about the reconciliation of the realistic point of view and the formalistic one, and the particles being accompanied by the field would appear to be as real an existence as any other particles known in physics. Recently, the p(esent author tried to intlOduce a hypothesis into the theory of negative energy Bose fields(3,. A brief consideration was presented, but it is noy yet to give a full account on it. Now, we shall give detailed accounts of the underlying idea, which is a close analogon to Dirac's positron theory.