Physics
Scientific paper
Sep 1966
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1966rspsa.294..175d&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 294, Issue 1437, pp. 175-194
Physics
12
Scientific paper
The self-consistency problems arising when massless particles of higher spin are coupled to the electromagnetic and gravitational fields are investigated using a group theoretic method as opposed to the Lagrangian approach employed by Fierz & Pauli (1939) in their discussion for massive particles. A massless particle of spin j is described by a 4j dimensional vector satisfying a generalization of Rumer's equation (1930). 2j + 1 of these 4j components form the conventional quantity associated with a particle of spin j and the remaining 2j - 1 are supernumary quantities needed for the consistency of the interacting system; the whole object transforms according to the reduced representation (j, 0)bigoplus(j - 1, 0) of the homogeneous Lorentz group. It is suggested that this formalism is a convenient way of writing higher-spin equations in particle-like form with attendant advantages (see. for example, Good 1959). In the force-free case the 2j - 1 auxiliary quantities can be set equal to zero but this is not possible in the interacting system without inconsistency. One conclusion is that it is impossible for a (massless) particle of unique spin to be coupled minimally to gravitation unless either its spin is less than 3/2, space-time is conformally flat or its spin is two and it describes gravitation radiation itself.
Dowker J. S.
Dowker Yih P.
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