This booklet explains the gang illustration concept for quantum idea within the language of quantum thought. As is widely known, staff illustration idea is particularly powerful software for quantum idea, specifically, angular momentum, hydrogen-type Hamiltonian, spin-orbit interplay, quark version, quantum optics, and quantum details processing together with quantum mistakes correction.

To describe a major photograph of program of illustration conception to quantum conception, the ebook must comprise the subsequent six issues, permutation team, SU(2) and SU(d), Heisenberg illustration, squeezing operation, Discrete Heisenberg illustration, and the relation with Fourier remodel from a unified point of view by way of together with projective illustration. regrettably, even if there are such a lot of solid mathematical books for part of six issues, no e-book comprises all of those subject matters simply because they're too segmentalized. extra, a few of them are written in an summary method in mathematical type and, usually, the fabrics are too segmented. not less than, the notation isn't really wide-spread to humans operating with quantum theory.

Others are sturdy hassle-free books, yet don't take care of subject matters regarding quantum conception. particularly, such trouble-free books don't disguise projective illustration, that's extra vital in quantum idea. nevertheless, there are a number of books for physicists. even though, those books are too uncomplicated and shortage the distinctive dialogue. therefore, they aren't necessary for complex learn even in physics.

To unravel this factor, this publication begins with the elemental arithmetic for quantum idea. Then, it introduces the fundamentals of staff illustration and discusses the case of the finite teams, the symmetric staff, e.g. subsequent, this publication discusses Lie crew and Lie algebra. This half starts off with the fundamentals wisdom, and proceeds to the certain teams, e.g., SU(2), SU(1,1), and SU(d). After the certain teams, it explains concrete functions to actual platforms, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interplay, and quark version.

Then, it proceeds to the final conception for Lie crew and Lie algebra. utilizing this data, this e-book explains the Bosonic process, which has the symmetries of Heisenberg team and the squeezing symmetry through SL(2,R) and Sp(2n,R). eventually, because the discrete model, this e-book treats the discrete Heisenberg illustration that's on the topic of quantum blunders correction. to augment readers' undersnding, this ebook includes fifty four figures, 23 tables, and 111 routines with solutions.