Abstract
The second-rank tensor field φμν is decomposed into its various subspaces under the Lorentz group and the appropriate projection operators are exhibited explicitly. The most general local, Hermitian, free-field Lagrangian which can be formed from this field is written down, and the corresponding equations of motion and subsidiary conditions are derived by means of a variational principle. Finally some possible applications of this theory are discussed (in particular spin-2 boson theory), and all the possible couplings of this field to a Dirac particle are listed in full.
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