Mathews, P. M. ; Govindarajan, T. R.
(1982)
*The lower bound on the minimal degree of the matrices in first-order relativistic wave equations*
Journal of Physics A: Mathematical and General, 15
(7).
pp. 2093-2100.
ISSN 0305-4470

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Official URL: http://iopscience.iop.org/0305-4470/15/7/020

Related URL: http://dx.doi.org/10.1088/0305-4470/15/7/020

## Abstract

A proof is given, on the basis of a theorem due to Garding (1944), for a lower bound on the degree (l+2) of the minimal equation of matrices beta ^{mu} in first-order unique-mass relativistic wave equations. It is not necessary, for the applicability of the theorem, that a hermitising operator should exist or that the equation be irreducible; and the generalisation of the bound to multimass equations is also straightforward. The bound is not, in general, linked to the physical spin or spins s allowed by the wave equation or the maximum spin j_{m} contained in the wavefunction. However, in the physically important case of irreducible equations which admit a hermitising operator, the bound becomes (l+2)>or= (2j_{m}+1), which is stronger than the bound (2s+1) suggested in the recent literature.

Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Physics Publishing. |

ID Code: | 20551 |

Deposited On: | 20 Nov 2010 14:20 |

Last Modified: | 06 Jun 2011 09:01 |

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