Canonical conjugate momentum of discrete label operators in quantum mechanics I: formalism

We discuss the inadequacy of the standard definition of canonical conjugation for a quantum operator having adiscrete spectrum. A different definition is proposed, based on the analogy betweencontinuous anddiscrete translations (or rotations). This definition can be applied to special operators which we calllabel operators. The general form of the conjugate momentum of a label operator is found and the resulting canonical commutation rules are discussed. It is shown that the canonical commutator acts like ac number in itsdomain _I , but the domain does not coincide with the whole Hilbert space. The properties of the subspace _I are also discussed.