Your language?
Nov, 2017
Sun Mon Tue Wed Thu Fri Sat
1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30

数理物理における離散あるいは組み合せ論的モデル

なため , では のために いら れてきた その つの アプロ として がある

する つの 方法 であるが , における アプロ , えば , Fukuma, Hosono, Kawai [ FHK94 ] , Lauda Pfeiffer [ LP07 ] , Mnëv [ Mnë09 ] などで 使 われている これらの アプロ Pachner 仕事 [ Pac91 ] このような 研究 のために より しているのは Balsam Kirillov [ KJB ] ある

Quantum gravity への アプロ としては , Regge Williams survey [ RW00 ] Ambjorn, Durhuus, Jonsson [ ADJ97 ] がある これらでも 使 われている

  • discrete quantum gravity

これらについては , Benedetti Ziegler [ BZ11 ] Benedetti [ AB ]

, では モデル 使 われてきた グラフ モデ がよく 使 われているように

への アプロ として , Díaz Villamarín [ DV ] Frigg らの [ Fri08 FW11 ] , Giles [ Gil64 ] Gromov [ Gro ] , Jaynes [ Jay63 ] , Lesne [ Les14 ] , Lieb Yngvason [ LY98 ] げている また , entropy への アプロ として Niven 仕事 [ Niv05 Niv Niv09 ] げて いる

References

[AB]     Karim Adiprasito and Bruno Benedetti. Collapsibility of CAT(0) spaces, arXiv:1107.5789 .

[ADJ97]     Jan Ambjørn, Bergfinnur Durhuus, and Thordur Jonsson. Quantum geometry . Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, 1997, http://dx.doi.org/10.1017/CBO9780511524417 . A statistical field theory approach.

[BZ11]     Bruno Benedetti and Günter M. Ziegler. On locally constructible spheres and balls. Acta Math. , 206(2):205–243, 2011, arXiv:0902.0436 .

[DV]     Rafael Diaz and Sergio Villamarin. Combinatorial Micro-Macro Dynamical Systems, arXiv:1507.06703 .

[FHK94]     M. Fukuma, S. Hosono, and H. Kawai. Lattice topological field theory in two dimensions. Comm. Math. Phys. , 161(1):157–175, 1994, arXiv:hep-th/9212154 .

[Fri08]     Roman Frigg. A field guide to recent work on the foundations of statistical mechanics. In The Ashgate companion to contemporary philosophy of physics , pages 99–196. Ashgate, Aldershot, 2008.

[FW11]     Roman Frigg and Charlotte Werndl. Entropy: a guide for the perplexed. In Probabilities in physics , pages 115–142. Oxford Univ. Press, Oxford, 2011, http://dx.doi.org/10.1093/acprof:oso/9780199577439.003.0005 .

[Gil64]     R. Giles. Mathematical foundations of thermodynamics . International Series of Monographs on Pure and Applied Mathematics, Vol. 53. A Pergamon Press Book. The Macmillan Co., New York, 1964.

[Gro]     Misha Gromov. In a Search for a Structure, Part 1: On Entropy, http://www.ihes.fr/ ~ gromov/PDF/structre-serch-entropy-july5-2012.pdf .

[Jay63]     E. T. Jaynes. Information theory and statistical mechanics. In Statistical physics (Brandeis Summer Institute, 1962, Vol. 3) , pages 181–218. W. A. Benjamin, New York, 1963.

[KJB]     Alexander Kirillov Jr. and Benjamin Balsam. Turaev-Viro invariants as an extended TQFT, arXiv:1004.1533 .

[Les14]     Annick Lesne. Shannon entropy: a rigorous notion at the crossroads between probability, information theory, dynamical systems and statistical physics. Math. Structures Comput. Sci. , 24(3):e240311, 63, 2014, http://dx.doi.org/10.1017/S0960129512000783 .

[LP07]     Aaron D. Lauda and Hendryk Pfeiffer. State sum construction of two-dimensional open-closed topological quantum field theories. J. Knot Theory Ramifications , 16(9):1121–1163, 2007, arXiv:math/0602047 .

[LY98]     Elliott H. Lieb and Jakob Yngvason. A guide to entropy and the second law of thermodynamics. Notices Amer. Math. Soc. , 45(5):571–581, 1998.

[Mnë09]     P. Mnëv. Notes on simplicial BF theory. Mosc. Math. J. , 9(2):371–410, back matter, 2009, arXiv:hep-th/0610326 .

[Niv]     Robert K. Niven. Origins of the Combinatorial Basis of Entropy, arXiv:0708.1861 .

[Niv05]     Robert K. Niven. Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Phys. Lett. A , 342(4):286–293, 2005, arXiv:cond-mat/0412460 .

[Niv09]     R. K. Niven. Combinatorial entropies and statistics. Eur. Phys. J. B , 70(1):49–63, 2009, arXiv:0902.3038 .

[Pac91]     Udo Pachner. P.L. homeomorphic manifolds are equivalent by elementary shellings. European J. Combin. , 12(2):129–145, 1991, http://dx.doi.org/10.1016/S0195-6698(13)80080-7 .

[RW00]     Tullio Regge and Ruth M. Williams. Discrete structures in gravity. J. Math. Phys. , 41(6):3964–3984, 2000, arXiv:gr-qc/0012035 .