By Predrag Cvitanović
If classical Lie teams safeguard bilinear vector norms, what Lie teams protect trilinear, quadrilinear, and better order invariants? Answering this question from a clean and unique viewpoint, Predrag Cvitanovic takes the reader at the notable, four-thousand-diagram trip during the idea of Lie teams. This e-book is the 1st to systematically enhance, clarify, and follow diagrammatic projection operators to build all semi-simple Lie algebras, either classical and exceptional.
The invariant tensors are awarded in a slightly unconventional, yet in recent times primary, "birdtracks" notation encouraged by means of the Feynman diagrams of quantum box thought. particularly, invariant tensor diagrams substitute algebraic reasoning in conducting all group-theoretic computations. The diagrammatic strategy is very powerful in comparing complex coefficients and team weights, and revealing symmetries hidden through traditional algebraic or index notations. The booklet covers so much issues wanted in functions from this new point of view: variations, younger projection operators, spinorial representations, Casimir operators, and Dynkin indices. past this well-traveled territory, extra unique vistas open up, equivalent to "negative dimensional" kinfolk among quite a few teams and their representations. the main exciting results of classifying primitive invariants is the emergence of all remarkable Lie teams in one relations, and the attendant development of outstanding and classical Lie teams, the so-called Magic Triangle. Written in a full of life and personable type, the e-book is aimed toward researchers and graduate scholars in theoretical physics and mathematics.