By Masahito Hayashi

ISBN-10: 3319449044

ISBN-13: 9783319449043

ISBN-10: 3319449060

ISBN-13: 9783319449067

This ebook explains the gang illustration idea for quantum idea within the language of quantum concept. As is widely known, workforce illustration conception is particularly powerful device for quantum idea, specifically, angular momentum, hydrogen-type Hamiltonian, spin-orbit interplay, quark version, quantum optics, and quantum info processing together with quantum mistakes correction.

To describe a massive photograph of program of illustration idea to quantum conception, the ebook must comprise the subsequent six subject matters, permutation workforce, SU(2) and SU(d), Heisenberg illustration, squeezing operation, Discrete Heisenberg illustration, and the relation with Fourier remodel from a unified standpoint via together with projective illustration. regrettably, even supposing there are such a lot of sturdy mathematical books for part of six subject matters, no ebook comprises all of those issues simply because they're too segmentalized. extra, a few of them are written in an summary approach in mathematical sort and, usually, the fabrics are too segmented. a minimum of, the notation isn't really universal to humans operating with quantum theory.

Others are stable simple books, yet don't care for themes relating to quantum thought. particularly, such basic books don't conceal projective illustration, that's extra very important in quantum concept. nonetheless, there are a number of books for physicists. although, those books are too uncomplicated and shortage the specified dialogue. consequently, they aren't beneficial for complicated learn even in physics.

To get to the bottom of this factor, this publication begins with the fundamental arithmetic for quantum idea. Then, it introduces the fundamentals of workforce illustration and discusses the case of the finite teams, the symmetric staff, e.g. subsequent, this ebook discusses Lie team and Lie algebra. This half begins with the fundamentals wisdom, and proceeds to the exact teams, e.g., SU(2), SU(1,1), and SU(d). After the unique teams, it explains concrete purposes to actual platforms, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interplay, and quark version.

Then, it proceeds to the overall thought for Lie team and Lie algebra. utilizing this data, this publication explains the Bosonic process, which has the symmetries of Heisenberg workforce and the squeezing symmetry by way of SL(2,R) and Sp(2n,R). ultimately, because the discrete model, this ebook treats the discrete Heisenberg illustration that's on the topic of quantum blunders correction. to augment readers' undersnding, this publication includes fifty four figures, 23 tables, and 111 routines with solutions.