SL(2, C) Representations in Explicitly ``Energy-Dependent'' Basis. I

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Unitary and nonunitary representations of the SL(2, C) group are investigated in such a basis, in which the subgroup diagonalized is that one which in the four-dimensional representation leaves invariant the 4-vector pμ = (½(1 + v), 0, 0, ½(1 − v)) for an arbitrary real value of Pμ2=v. The split of the representation space into irreducible subspaces changes smoothly when varying the value of v. The formalism is of importance in physical theories which postulate analyticity requirements and Lorentz invariance simultaneously (e.g., Regge and Lorentz pole theory). In this paper we construct explicit basis functions of the representation spaces.