ローレンツ群 関連項目

ウィキペディア

ローレンツ群

出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2023/07/11 21:12 UTC 版)

関連項目

• ローレンツ変換
• ローレンツ群の表現論
• ポアンカレ群
• メビウス群
• ミンコフスキー空間
• 複四元数

• 不定値直交群
• 四元数と空間回転
• 相対論的重心
• 特殊相対性理論
• 量子力学における対称性

参照文献

• Artin, Emil (1957). Geometric Algebra. New York: Wiley. ISBN 0-471-60839-4  See Chapter III for the orthogonal groups O(p, q).
• Carmeli, Moshe (1977). Group Theory and General Relativity, Representations of the Lorentz Group and Their Applications to the Gravitational Field. McGraw-Hill, New York. ISBN 0-07-009986-3  A canonical reference; see chapters 1–6 for representations of the Lorentz group.
• Frankel, Theodore (2004). The Geometry of Physics (2nd Ed.). Cambridge: Cambridge University Press. ISBN 0-521-53927-7  An excellent resource for Lie theory, fiber bundles, spinorial coverings, and many other topics.
• Fulton, William; Harris, Joe (1991), Representation theory. A first course, Graduate Texts in Mathematics, Readings in Mathematics, 129, New York: Springer-Verlag, ISBN 978-0-387-97495-8, MR1153249, ISBN 978-0-387-97527-6  See Lecture 11 for the irreducible representations of SL(2, C).
• Gelfand, I.M.; Minlos, R.A.; Shapiro, Z.Ya. (1963), Representations of the Rotation and Lorentz Groups and their Applications, New York: Pergamon Press 
• Hall, G. S. (2004). Symmetries and Curvature Structure in General Relativity. Singapore: World Scientific. ISBN 981-02-1051-5  See Chapter 6 for the subalgebras of the Lie algebra of the Lorentz group.
• Hatcher, Allen (2002). Algebraic topology. Cambridge: Cambridge University Press. ISBN 0-521-79540-0  See also the “online version”. 2005年7月3日閲覧。 See Section 1.3 for a beautifully illustrated discussion of covering spaces. See Section 3D for the topology of rotation groups.
• Naber, Gregory (1992). The Geometry of Minkowski Spacetime. New York: Springer-Verlag. ISBN 0486432351  (Dover reprint edition.) An excellent reference on Minkowski spacetime and the Lorentz group.
• Needham, Tristan (1997). Visual Complex Analysis. Oxford: Oxford University Press. ISBN 0-19-853446-9  See Chapter 3 for a superbly illustrated discussion of Möbius transformations.
• Wigner, E. P. (1939), “On unitary representations of the inhomogeneous Lorentz group”, Annals of Mathematics 40 (1): 149–204, Bibcode: 1939AnMat..40..922E, doi:10.2307/1968551, MR1503456 .