Abstract
The Rarita-Schwinger equation for a spin- particle with minimal electromagnetic coupling is solved completely in the case when a constant homogeneous external magnetic field is present. It is shown that the spectrum of energy eigenvalues includes complex values if is such that , and further that the norm of the Rarita-Schwinger wave function (i.e., the total "charge" integral defined from the Lagrangian) which is positive definite for becomes indefinite (even after taking account of the constraints) when exceeds unity. These results confirm that the difficulties in quantization first discovered by Johnson and Sudarshan are a reflection of the indefiniteness of the norm which appears already at the -number level, and suggest that the nature of the energy spectrum (whether or not complex values are present) in the presence of very large magnetic fields would provide a quick means of predicting whether such difficulties would arise in quantization.
- Received 7 January 1975
DOI:https://doi.org/10.1103/PhysRevD.12.458
©1975 American Physical Society