Communications in Mathematical Physics
, Volume 18, Issue 2, pp 97108
First online:
The BargmannWigner method in Galilean relativity
 C. R. HagenAffiliated withDepartment of Physics and Astronomy, University of Rochester
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The equations of motion of a spin one particle as derived from LevyLeblond's Galilean formulation of the BargmannWigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the BargmannWigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling.
More generally it is demonstrated that one can replace LevyLeblond's version of the BargmannWigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the BargmannWigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the BargmannWigner set is found to have only a somewhat trivial counterpart in the Galilean case.
 Title
 The BargmannWigner method in Galilean relativity
 Journal

Communications in Mathematical Physics
Volume 18, Issue 2 , pp 97108
 Cover Date
 197006
 DOI
 10.1007/BF01646089
 Print ISSN
 00103616
 Online ISSN
 14320916
 Publisher
 SpringerVerlag
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 Authors

 C. R. Hagen ^{(1)}
 Author Affiliations

 1. Department of Physics and Astronomy, University of Rochester, Rochester, New York