LEADER 05134nam 22006135 450 001 9910151662703321 005 20251116173402.0 010 $a3-319-44906-0 024 7 $a10.1007/978-3-319-44906-7 035 $a(CKB)3710000000952851 035 $a(DE-He213)978-3-319-44906-7 035 $a(MiAaPQ)EBC4746019 035 $a(PPN)197140866 035 $a(EXLCZ)993710000000952851 100 $a20161118d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGroup representation for quantum theory /$fby Masahito Hayashi 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XXVIII, 338 p. 54 illus., 1 illus. in color.) 311 08$a3-319-44904-4 320 $aIncludes bibliographical references and index. 327 $aFoundation of Quantum Theory -- Group Representation -- Representations of Lie Group and Lie Algebra (Basics) -- Representations of Lie Group and Lie Algebra (Special Case) -- Representations of Lie Group and Lie Algebra (General Case) -- Bosonic System -- Discretization of Bosonic System. 330 $aThis book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, the materials are too segmented. At least, the notation is not familiar to people working with quantum theory. Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, and quark model. Then, it proceeds to the general theory for Lie group and Lie algebra. Using this knowledge, this book explains the Bosonic system, which has the symmetries of Heisenberg group and the squeezing symmetry by SL(2,R) and Sp(2n,R). Finally, as the discrete version, this book treats the discrete Heisenberg representation which is related to quantum error correction. To enhance readers' undersnding, this book contains 54 figures, 23 tables, and 111 exercises with solutions. 606 $aQuantum theory 606 $aGroup theory 606 $aQuantum computers 606 $aSpintronics 606 $aMathematical physics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aQuantum Information Technology, Spintronics$3https://scigraph.springernature.com/ontologies/product-market-codes/P31070 606 $aQuantum Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/M14070 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aQuantum theory. 615 0$aGroup theory. 615 0$aQuantum computers. 615 0$aSpintronics. 615 0$aMathematical physics. 615 14$aQuantum Physics. 615 24$aGroup Theory and Generalizations. 615 24$aQuantum Information Technology, Spintronics. 615 24$aQuantum Computing. 615 24$aMathematical Physics. 676 $a530.12 700 $aHayashi$b Masahito$4aut$4http://id.loc.gov/vocabulary/relators/aut$0817794 906 $aBOOK 912 $a9910151662703321 996 $a??????????$91830204 997 $aUNINA