Unitary Symmetry and Combinatorics by James D Louck (PDF)

Description

This monograph integrates unitary symmetry and combinatorics, showing in great detail how the coupling of angular momenta in quantum mechanics is related to binary trees, trivalent trees, cubic graphs, MacMahon’s master theorem, and other basic combinatorial concepts. A comprehensive theory of recoupling matrices for quantum angular momentum is developed. For the general unitary group, polynomial forms in many variables called matrix Schur functions have the remarkable property of giving all irreducible representations of the general unitary group and are the basic objects of study. The structure of these irreducible polynomials and the reduction of their Kronecker product is developed in detail, as is the theory of tensor operators.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is a masterpiece! It is a great proof that everything is related, and thatNatute, when analyzed deeply, reduces to combinatorics. One particulary attractivetidbit was the pointing out that MacMahon’s Master theorem is important in physics, and in fact a variant of it was rediscovered by nobelist Julian Schwinger of QED fame.This book is too long to be read cover-to-cover, but it is so well-written thatif you open it at any chapter, it would still be understandable. This is the mostcomprehensive treatment of the Racah symbol I am aware of. Anyone who is interested inseeing how algebraic combinatorics can be used effectively in mathematical physics, should read at least parts of this book.

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