This e-book explains the gang illustration concept for quantum concept within the language of quantum concept. As is celebrated, staff illustration conception is particularly powerful software for quantum idea, particularly, angular momentum, hydrogen-type Hamiltonian, spin-orbit interplay, quark version, quantum optics, and quantum details processing together with quantum errors correction.

To describe a tremendous photograph of software of illustration thought to quantum idea, the ebook must include the next six subject matters, permutation staff, SU(2) and SU(d), Heisenberg illustration, squeezing operation, Discrete Heisenberg illustration, and the relation with Fourier rework from a unified standpoint through together with projective illustration. regrettably, even though there are such a lot of strong mathematical books for part of six subject matters, no booklet includes all of those issues simply because they're too segmentalized. additional, a few of them are written in an summary manner in mathematical sort and, frequently, the fabrics are too segmented. no less than, the notation isn't really time-honored to humans operating with quantum theory.

Others are sturdy basic books, yet don't care for subject matters on the topic of quantum concept. specifically, such hassle-free books don't hide projective illustration, that is extra very important in quantum thought. nevertheless, there are a number of books for physicists. besides the fact that, those books are too basic and shortage the special dialogue. for this reason, they don't seem to be worthwhile for complicated research even in physics.

To get to the bottom of this factor, this ebook starts off with the fundamental arithmetic for quantum thought. Then, it introduces the fundamentals of team illustration and discusses the case of the finite teams, the symmetric staff, e.g. subsequent, this e-book discusses Lie workforce and Lie algebra. This half begins with the fundamentals wisdom, and proceeds to the detailed teams, e.g., SU(2), SU(1,1), and SU(d). After the distinctive 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 thought for Lie workforce and Lie algebra. utilizing this information, this booklet explains the Bosonic approach, which has the symmetries of Heisenberg staff and the squeezing symmetry by means of SL(2,R) and Sp(2n,R). eventually, because the discrete model, this booklet treats the discrete Heisenberg illustration that's concerning quantum blunders correction. to reinforce readers' undersnding, this booklet includes fifty four figures, 23 tables, and 111 workouts with solutions.