Bhabha first-order wave equations. V. Indefinite metric and Foldy-Wouthuysen transformations. [Indefinite metric]
We prove the existence of a Foldy-Wouthuysen (FW) transformation which decouples the mass states of all the Bhabha Poincare generators and diagonalizes the Hamiltonian. Since the Bhabha fields operate in an indefinite-metric space, such an existence is not a priori guaranteed. The FW-transformed generators are given and satisfy the Poincare Lie algebra. We observe that although the FW transformation expressed as a power series in c/sup -1/ more clearly exhibits the physics of the situation, it is only in the Dirac and Duffin-Kemmer-Petiau special cases of the Bhabha fields that the FW-transformation power series can easily be summed to yield closed-form expression. The general closed-form expression surrenders more readily to another technique. Therefore, as a first calculation, in this paper we present a method of generating the FW transformation as a power series in c/sup -1/. Our discussion concentrates on the indefinite metric, the physics which is evident in the power-series form (such as size and types of Zitterbewegung), and on a detailed examination of special cases up to spin 3/2. In all the above, a special handling of the built-in subsidiary components of the integer-spin fields is once again necessary. We also comment on what the indefinite metric may be implying about the possibility of finding a totally consistent high-spin field theory. In a later paper we present a derivation of the exact, closed-form transformation. (AIP)
- Research Organization:
- Theoretical Division, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
- OSTI ID:
- 7356168
- Journal Information:
- Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 14:2; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
Similar Records
Foldy-Wouthuysen transformations in an indefinite-metric space. I. Necessary and sufficient conditions for existence
Foldy-Wouthuysen transformations in an indefinite-metric space. III. Relation to Lorentz transformations for first-order wave equations and the Poincare generators