Tensor properties of second-quantization operators and analysis of composite physical systems

A covar[ant formulation of the method of second quantization is proposed on the basis of differentiation in the algebra of boson operators and their tensor properties; it enables one to take into account explicitly the symmetry properties of the investigated objects. As an application of the method, the general scheme is given for constructing a unified closed formalism for the groups $SU_n$ that significantly simplifies the calculation of the generating invariants, the normalized Clebsch–Gordan coefficients and their combinations. The results obtained are important for analyzing composite systems and coherent phenomena.