Irreducible Tensorial Sets by U. Fano | (PDF) Free Download

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Irreducible Tensorial Sets discusses mathematical methods originating from the theory of coupling and recoupling of angular momenta in atomic physics that constitute an extension of vector and tensor algebra. The book presents a unified treatment with a compact system of notations from different approaches, such as group theory, algebra, and quantum mechanical transformation theory. It discusses irreducible tensorial sets that cover different sets of quantities such as tensor components and states of atomic systems. It also explains quantum mechanical applications, coupling and recoupling of atomic and nuclear states, the Wigner-Eckart theorem, and the products of tensorial sets of operators. The text shows how to calculate the interaction energy between atomic systems couple with one another with a constant total angular momentum. The book also explains the correlations which are functions of the Euler angles between the frame of reference in which a radiation is observed and a frame of reference attached to the orienting radiation or field. It then cites sample problems related to the angular distribution of radiations. The book will prove useful for physicists, for mathematicians, or for readers with some knowledge in theoretical physics, particularly on theory of groups and quantum mechanics.

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⭐This book should be reprinted e.g. in Dover. This book provides full descriptions of how the angular momentum theory should be made, what sign convention e.g. for J+ should be taken. It describes why co- and contragredient basis sets should be considered. With that distinction of contragredience and cogredience, the tensorial sets can be introduced in Liouville space. His famous angular momentum transfer teory naturally enters into the theory of angular momentum theory, greatly simplifying the description of geometrical aspects of physical processes. Chap. 19 provides the complete description for the atomic processes interacting with photons which are not condensed into the simple form experimentalists can use, The simplified form useful to the experimentalists was attained in his famous review article with Prof. Macek (Rev. Mod. Phys. 45, 553 (1973)). Appendix H, I and J are very inciteful, should be a source for further development of angular momentum theory. His theory for the construction of antisymmetrized wave functions for the general atomic configurations completes the elementary treatment in p69-75 in this book and was used by Hibbert for the famous C.F. Fischer’s MCHF program. When he wrote this book with Prof. Racah in the hotel room, they could not find the suitable mathematical theory to which this theory can be described. They therefore simply chose “irreducible tensorial sets” as the title for their theory. Fano’s efforts in this direction in his later years can be found in his book “Symmetries in Quantum Mechanics” with A.R.P. Rau.

⭐Es un libro, que partiendo desde el inicio de conjunto tensorial en la primera parte, explica claramente la invariancia de diversos productos, los productos irreducibles de conjuntos y sus coeficientes asociados. En la segunda parte aplica lo visto antes a diversos sistemas cuánticos. En los apéndices va aclarando todos los conceptos y métodos necesarios para poder aprovechar lo explicado, en el caso que algo no se sepa o no se recuerde.

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