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In mathematics, a Generalized Clifford algebra (GCA) is an associative algebra that generalizes the Clifford algebra, and goes back to the work of Hermann Weyl,〔Weyl, H., "Quantenmechanik und Gruppentheorie", ''Zeitschrift für Physik'', 46 (1927) pp. 1–46, . Weyl, H., ''The Theory of Groups and Quantum Mechanics'' (Dover, New York, 1931)〕 who utilized and formalized these clock-and-shift operators introduced by J. J. Sylvester (1882),〔Sylvester, J. J., (1882), ''Johns Hopkins University Circulars'' I: 241-242; ibid II (1883) 46; ibid III (1884) 7–9. Summarized in ''The Collected Mathematics Papers of James Joseph Sylvester'' (Cambridge University Press, 1909) v III . (online ) and ( further ). 〕 and organized by Cartan (1898)〔Cartan, E. (1898). "Les groupes bilinéaires et les systèmes de nombres complexes." ''Annales de la faculté des sciences de Toulouse'' 12.1 B65-B99. (online )〕 and Schwinger.〔Schwinger, J. (1960), "Unitary operator bases", ''Proc Natl Acad Sci U S A'', April; 46(4): 570–579, PMCID: PMC222876; ''ibid'', "Unitary transformations and the action principle", 46(6): 883–897, PMCID: PMC222951〕 Clock and shift matrices find routine applications in numerous areas of mathematical physics, providing the cornerstone of quantum mechanical dynamics in finite-dimensional vector spaces.〔〔A. K. Kwaśniewski: ''On Generalized Clifford Algebra C4(n) and GLq(2;C) quantum group''〕 The concept of a spinor can further be linked to these algebras.〔 The term Generalized Clifford Algebras can also refer to associative algebras that are constructed using forms of higher degree instead of quadratic forms. == Definition and properties == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Generalized Clifford algebra」の詳細全文を読む スポンサード リンク
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