The principal development in this paper is the extension of the eigenvalue-eigenvector concept to complete sets of anticommuting operators. With the aid of this formalism we construct a transformation function for the Dirac field, as perturbed by an external source. This transformation function is enlarged to describe phase transformations and, when applied to the isolated Dirac field, yields the charge and energy-momentum eigenvalues and eigenfunctions. The transformation function describing the system in the presence of the source is then used as a generating function to construct the matrices of all ordered products of the field operators, for the isolated Dirac field. The matrices in the occupation number representation are exhibited with a classification that effectively employs a time-reversed description for negative frequency modes. The last section supplements III by constructing the matrices of all ordered products of the potential vector, for the isolated electromagnetic field.
- Received 6 August 1953
- Published in the issue dated December 1953
© 1953 The American Physical Society