메뉴 건너뛰기




Volumn 42, Issue 7, 2012, Pages 819-855

Division Algebras and Quantum Theory

Author keywords

Convex cone; Division algebra; Duality; Group representation; Jordan algebra; Octonion; Quantum theory; Quaternion

Indexed keywords


EID: 84861583874     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10701-011-9566-z     Document Type: Article
Times cited : (93)

References (47)
  • 1
    • 26944485450 scopus 로고    scopus 로고
    • Abstract scalars, loops, and free traced and strongly compact closed categories
    • Lecture Notes in Computer ScienceAlso available at, Berlin: Springer
    • Abramsky, S.: Abstract scalars, loops, and free traced and strongly compact closed categories. In: Proceedings of CALCO 2005. Lecture Notes in Computer Science, vol. 3629, pp. 1-31. Springer, Berlin (2005). Also available at http://web. comlab. ox. ac. uk/oucl/work/samson. abramsky/calco05. pdf.
    • (2005) Proceedings of CALCO 2005 , vol.3629 , pp. 1-31
    • Abramsky, S.1
  • 7
    • 84861616284 scopus 로고    scopus 로고
    • Symplectization, complexification and mathematical trinities
    • E. Bierstone, B. Khesin, A. Khovanskii, and J. E. Marsden (Eds.), Providence: AMS
    • Arnold, V. I.: Symplectization, complexification and mathematical trinities. In: Bierstone, E., Khesin, B., Khovanskii, A., Marsden, J. E. (eds.) The Arnoldfest: Proceedings of a Conference in Honour of V. I. Arnold for His Sixtieth Birthday. AMS, Providence (1999).
    • (1999) The Arnoldfest: Proceedings of a Conference in Honour of V.I. Arnold for His Sixtieth Birthday
    • Arnold, V.I.1
  • 8
    • 0031562874 scopus 로고    scopus 로고
    • Higher-dimensional algebra II: 2-Hilbert spaces
    • Also available as arXiv:q-alg/9609018
    • Baez, J.: Higher-dimensional algebra II: 2-Hilbert spaces. Adv. Math. 127, 125-189 (1997). Also available as arXiv: q-alg/9609018.
    • (1997) Adv. Math. , vol.127 , pp. 125-189
    • Baez, J.1
  • 9
    • 0035997407 scopus 로고    scopus 로고
    • The octonions
    • Errata in Bull. Am. Math. Soc. 42, 213 (2005). Also available as arXiv:math/0105155
    • Baez, J.: The octonions. Bull. Am. Math. Soc. 39, 145-205 (2002). Errata in Bull. Am. Math. Soc. 42, 213 (2005). Also available as arXiv: math/0105155.
    • (2002) Bull. Am. Math. Soc. , vol.39 , pp. 145-205
    • Baez, J.1
  • 10
    • 40849149542 scopus 로고    scopus 로고
    • Quantum quandaries: a category-theoretic perspective
    • Also available as arXiv:quant-ph/0404040, S. French, D. Rickles, and J. Saatsi (Eds.), Oxford: Oxford University Press
    • Baez, J.: Quantum quandaries: a category-theoretic perspective. In: French, S., Rickles, D., Saatsi, J. (eds.) Structural Foundations of Quantum Gravity, pp. 240-265. Oxford University Press, Oxford (2006). Also available as arXiv: quant-ph/0404040.
    • (2006) Structural Foundations of Quantum Gravity , pp. 240-265
    • Baez, J.1
  • 11
    • 84861645529 scopus 로고    scopus 로고
    • Division algebras and supersymmetry I
    • Proc. Symp. Pure Math.Also available as arXiv:0909.0551, R. Doran, G. Friedman, and J. Rosenberg (Eds.), Providence: AMS
    • Baez, J., Huerta, J.: Division algebras and supersymmetry I. In: Doran, R., Friedman, G., Rosenberg, J. (eds.) Superstrings, Geometry, Topology, and C*-Algebras. Proc. Symp. Pure Math., vol. 81, pp. 65-80. AMS, Providence (2010). Also available as arXiv: 0909. 0551.
    • (2010) Superstrings, Geometry, Topology, and C*-Algebras , vol.81 , pp. 65-80
    • Baez, J.1    Huerta, J.2
  • 14
    • 79251503599 scopus 로고    scopus 로고
    • Physics, topology, logic and computation: a Rosetta Stone
    • Lecture Notes in PhysicsAlso available as arXiv:0903.0340, B. Coecke (Ed.), Berlin: Springer
    • Baez, J., Stay, M.: Physics, topology, logic and computation: a Rosetta Stone. In: Coecke, B. (ed.) New Structures for Physics. Lecture Notes in Physics, vol. 813, pp. 95-174. Springer, Berlin (2000). Also available as arXiv: 0903. 0340.
    • (2000) New Structures for Physics , vol.813 , pp. 95-174
    • Baez, J.1    Stay, M.2
  • 19
    • 0040677606 scopus 로고    scopus 로고
    • Chapter VIII, Sect. 7, Prop. 12, Berlin: Springer
    • Bourbaki, N.: Elements of Mathematics. Springer, Berlin (2008). Chapter VIII, Sect. 7, Prop. 12.
    • (2008) Elements of Mathematics
    • Bourbaki, N.1
  • 20
    • 0040677606 scopus 로고    scopus 로고
    • Chapter IX, Appendix II, Prop. 4, Berlin: Springer
    • Bourbaki, N.: Elements of Mathematics. Springer, Berlin (2008). Chapter IX, Appendix II, Prop. 4.
    • (2008) Elements of Mathematics
    • Bourbaki, N.1
  • 22
    • 84859090371 scopus 로고    scopus 로고
    • Lecture Notes in Physics, Berlin: Springer
    • Coecke, B.: New Structures for Physics. Lecture Notes in Physics, vol. 813. Springer, Berlin (2000).
    • (2000) New Structures for Physics , vol.813
    • Coecke, B.1
  • 23
    • 0005859447 scopus 로고
    • The exceptional Jordan algebra and the superstring
    • Also available at Project Euclid
    • Corrigan, E., Hollowood, T. J.: The exceptional Jordan algebra and the superstring. Commun. Math. Phys. 122, 393-410 (1989). Also available at Project Euclid.
    • (1989) Commun. Math. Phys. , vol.122 , pp. 393-410
    • Corrigan, E.1    Hollowood, T.J.2
  • 24
    • 0001755436 scopus 로고
    • The threefold way: algebraic structure of symmetry groups and ensembles in quantum mechanics
    • Dyson, F.: The threefold way: algebraic structure of symmetry groups and ensembles in quantum mechanics. J. Math. Phys. 3, 1199-1215 (1962).
    • (1962) J. Math. Phys. , vol.3 , pp. 1199-1215
    • Dyson, F.1
  • 26
    • 0007074553 scopus 로고
    • Über die reellen Darstellungen der endlichen Gruppen
    • Frobenius, F. G., Schur, I.: Über die reellen Darstellungen der endlichen Gruppen. Sitz. Akad. Preuss. Wiss. 186-208 (1906).
    • (1906) Sitz. Akad. Preuss. Wiss , pp. 186-208
    • Frobenius, F.G.1    Schur, I.2
  • 28
    • 84967782911 scopus 로고
    • Orthomodularity in infinite dimensions; a theorem of M. Solèr
    • Also available as arXiv:math/9504224
    • Holland, S. S. Jr.: Orthomodularity in infinite dimensions; a theorem of M. Solèr. Bull. Am. Math. Soc. 32, 205-234 (1995). Also available as arXiv: math/9504224.
    • (1995) Bull. Am. Math. Soc. , vol.32 , pp. 205-234
    • Holland Jr., S.S.1
  • 29
    • 0001935641 scopus 로고
    • Über die Composition der quadratischen Formen von beliebig vielen Variabeln
    • Hurwitz, A.: Über die Composition der quadratischen Formen von beliebig vielen Variabeln. Nachr. Ges. Wiss. Gött. 309-316 (1906).
    • (1906) Nachr. Ges. Wiss. Gött , pp. 309-316
    • Hurwitz, A.1
  • 30
    • 0005786052 scopus 로고
    • Über eine Klasse nichtassociativer hyperkomplexer Algebren
    • Jordan, P.: Über eine Klasse nichtassociativer hyperkomplexer Algebren. Nachr. Ges. Wiss. Gött. 569-575 (1932).
    • (1932) Nachr. Ges. Wiss. Gött , pp. 569-575
    • Jordan, P.1
  • 31
    • 0002266897 scopus 로고
    • On an algebraic generalization of the quantum mechanical formalism
    • Jordan, P., von Neumann, J., Wigner, E.: On an algebraic generalization of the quantum mechanical formalism. Ann. Math. 35, 29-64 (1934).
    • (1934) Ann. Math. , vol.35 , pp. 29-64
    • Jordan, P.1    von Neumann, J.2    Wigner, E.3
  • 38
    • 0000298707 scopus 로고
    • "Axiomatique" quantique
    • Piron, C.: "Axiomatique" quantique. Helv. Phys. Acta 37, 439-468 (1964).
    • (1964) Helv. Phys. Acta , vol.37 , pp. 439-468
    • Piron, C.1
  • 39
    • 84861612678 scopus 로고    scopus 로고
    • More on states and operators
    • Cambridge: Cambridge University Press
    • Polchinski, J.: More on states and operators. In: String Theory, vol. I. Cambridge University Press, Cambridge (1998).
    • (1998) String Theory, Vol. I
    • Polchinski, J.1
  • 40
    • 33847321487 scopus 로고    scopus 로고
    • Dagger compact closed categories and completely positive maps
    • Also available at, Elsevier: Amsterdam
    • Selinger, P.: Dagger compact closed categories and completely positive maps. In: Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005), pp. 139-163. Amsterdam, Elsevier (2007). Also available at http://www. mscs. dal. ca/~selinger/papers/#dagger.
    • (2007) Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005) , pp. 139-163
    • Selinger, P.1
  • 41
    • 21844491507 scopus 로고
    • Characterization of Hilbert spaces by orthomodular spaces
    • Solèr, M. P.: Characterization of Hilbert spaces by orthomodular spaces. Commun. Algebra 23, 219-243 (1995).
    • (1995) Commun. Algebra , vol.23 , pp. 219-243
    • Solèr, M.P.1
  • 42
    • 84968511114 scopus 로고
    • Absolute-valued algebras
    • Freely available online from the AMS
    • Urbanik, K., Wright, F. B.: Absolute-valued algebras. Proc. Am. Math. Soc. 11, 861-866 (1960). Freely available online from the AMS.
    • (1960) Proc. Am. Math. Soc. , vol.11 , pp. 861-866
    • Urbanik, K.1    Wright, F.B.2
  • 43
    • 60949110230 scopus 로고    scopus 로고
    • Propositional systems, Hilbert lattices and generalized Hilbert spaces
    • K. Engesser, D. M. Gabbay, and D. Lehmann (Eds.), Amsterdam: Elsevier
    • van Steirteghem, B., Stubbe, I.: Propositional systems, Hilbert lattices and generalized Hilbert spaces. In: Engesser, K., Gabbay, D. M., Lehmann, D. (eds.) Handbook of Quantum Logic and Quantum Structures: Quantum Structures. Elsevier, Amsterdam (2007).
    • (2007) Handbook of Quantum Logic and Quantum Structures: Quantum Structures
    • van Steirteghem, B.1    Stubbe, I.2
  • 46
    • 0010628193 scopus 로고
    • Homogeneous cones
    • Vinberg, E. B.: Homogeneous cones. Sov. Math. Dokl. 1, 787-790 (1961).
    • (1961) Sov. Math. Dokl. , vol.1 , pp. 787-790
    • Vinberg, E.B.1
  • 47
    • 0002423755 scopus 로고
    • On prime Jordan algebras. II
    • Zelmanov, E. I.: On prime Jordan algebras. II. Sib. Mat. Zh. 24, 89-104 (1983).
    • (1983) Sib. Mat. Zh. , vol.24 , pp. 89-104
    • Zelmanov, E.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.