The only book known to us giving an exposition of the algebra of non-commuting tensor operators and J-coefficients is Edmonds’ “Angular Momentum in Quantum Mechanics” (1957), which may serve as an excellent textbook for a first acquaintance with the subject. However, the exposition of the theory of J-coefficients and transformation matrices given in this book is not complete. This may constitute an impediment when the apparatus is employed in more complicated cases. The present book fills this gap.

The writing of this book began before Edmonds’ book appeared in print. The authors have utilized nearly all results known to them in the given field. Among these, a certain place is occupied by the results obtained by a group of workers under the direction of one of the present authors (A. Yutsis), the remaining two authors (I. Levinson and V. Vanagas) being the principal participants. The book corresponds to the content of the first part of a course, “Methods of Quantum-Mechanical Atomic Calculations,” given by the senior author to students of theoretical physics at the Vilnius State University lm. V. Kapsukas over the last two years.

We found it worthwhile to use the elegant and powerful methods of group theory in our exposition. To avoid encumbering the book with elements of group theory, we have assumed that the reader is already acquainted with linear representations of the three-dimensional rotation group. The reader who is unfamiliar with this may refer to the books by G.Ya. Lyubarsky (1957) and I. M. Gel’fand et al. (1958).

We begin with the well-known theory of vector addition of two angular momenta (Chapter I), turning next to the addition of an arbitrary number of angular momenta (Chapter II). The following chapters (III-VI) are devoted to quantities of the theory of angular momentum, where an important place is occupied by the graphical method, which is convenient for various calculations. The last chapter (VII) deals with the method of non-commuting tensor operators. Material of a supplementary character is given in the appendices.

We have cited a number of unpublished works, some of which were not available to us. References to these were based on other published works. We apologize in advance for any resulting inaccuracy.

Translation of
(Matematicheskn apparat teorn momenta kolichestva dvizheniya)
(Gosudarstvennoe lzdatel’stvo politicheskoi i nauchnoi literatury Litovskoi SSR) Vilnius 1960

Translated by A. Sen and R. N. Sen

You can get the book here and here