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Manifestly Covariant Approach to Bargmann-Wigner Fields (I): Generalized scalar products and Wigner states

Manifestly covariant formalism for Bargmann-Wigner fields is developed. It is shown that there exists some freedom in the choice of the form of the Bargmann-Wigner scalar product: The general product depends implicitly on a family of world-vectors. The standard choice of the product corresponds to timelike and equal vectors which define a ``time" direction. The generalized form shows that formulas are simpler if one chooses {\it null\/} directions. This freedom is used to derive simple covariant formulas for momentum-space wave functions (generalized Wigner states) corresponding to arbitrary mass and spin and using eigenstates of the Pauli-Lubanski vector. The eigenstates which make formulas the simplest correspond to projections of the Pauli-Lubanski vector on {\it null\/} directions. The new formulation is an alternative to the standard helicity formalism.