Rarita-Schwinger particles in homogeneous magnetic fields, and inconsistencies of spin-3/2 theories

Seetharaman, M. ; Prabhakaran, J. ; Mathews, P. M. (1975) Rarita-Schwinger particles in homogeneous magnetic fields, and inconsistencies of spin-3/2 theories Physical Review D, 12 (2). pp. 458-466. ISSN 0556-2821

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Official URL: http://link.aps.org/doi/10.1103/PhysRevD.12.458

Related URL: http://dx.doi.org/10.1103/PhysRevD.12.458

Abstract

The Rarita-Schwinger equation for a spin-3/2 particle with minimal electromagnetic coupling is solved completely in the case when a constant homogeneous external magnetic field H is present. It is shown that the spectrum of energy eigenvalues includes complex values if H is such that η=(2eH/3m3)>1, 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 η<1 becomes indefinite (even after taking account of the constraints) when η 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 c-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.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:20502
Deposited On:20 Nov 2010 14:24
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