A C * -dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking

Paula B. Cohen

Journal de théorie des nombres de Bordeaux (1999)

  • Volume: 11, Issue: 1, page 15-30
  • ISSN: 1246-7405

Abstract

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In this paper we extend to arbitrary number fields a construction of Bost-Connes of a C * -dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.

How to cite

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Cohen, Paula B.. "A $C^*$-dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking." Journal de théorie des nombres de Bordeaux 11.1 (1999): 15-30. <http://eudml.org/doc/248327>.

@article{Cohen1999,
abstract = {In this paper we extend to arbitrary number fields a construction of Bost-Connes of a $C^*$-dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.},
author = {Cohen, Paula B.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Bost-Connes theory; quantum theory; quantum statistical mechanics; Riemann zeta function; partition function; spontaneous symmetry breaking; Riemann hypothesis; -dynamical system; Dedekind zeta function},
language = {eng},
number = {1},
pages = {15-30},
publisher = {Université Bordeaux I},
title = {A $C^*$-dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking},
url = {http://eudml.org/doc/248327},
volume = {11},
year = {1999},
}

TY - JOUR
AU - Cohen, Paula B.
TI - A $C^*$-dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking
JO - Journal de théorie des nombres de Bordeaux
PY - 1999
PB - Université Bordeaux I
VL - 11
IS - 1
SP - 15
EP - 30
AB - In this paper we extend to arbitrary number fields a construction of Bost-Connes of a $C^*$-dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.
LA - eng
KW - Bost-Connes theory; quantum theory; quantum statistical mechanics; Riemann zeta function; partition function; spontaneous symmetry breaking; Riemann hypothesis; -dynamical system; Dedekind zeta function
UR - http://eudml.org/doc/248327
ER -

References

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  2. [BC] J-B. Bost and A. Connes, Hecke algebras, Type III factors and phase transitions with spontaneous symmetry breaking in number theory, Selecta Math. (New Series), 1 (1995), 411-457. Zbl0842.46040MR1366621
  3. [C] A. Connes, Formule de trace en géométrie non commutative et hypothèse de Riemann, C. R. Acad. Sci. Paris t.323, Série 1 (Analyse), (1996) 1231-1236. Zbl0864.46042MR1428542
  4. [HaLe] D. Harari and E. Leichtnam, Extension du phénomène de brisure spontanée de symétrie de Bost-Connes au cas des corps globaux quelconques, Selecta Mathematica, New Series 3 (1997), 205-243. Zbl0924.46051MR1466166
  5. [J] B. Julia, Statistical Theory of Numbers, in Number Theory and Physics, Les Houches Winter School, J-M. Luck, P. Moussa, M. Waldschmidt eds., Springer Proceedings in Physics 47 (1990), 276-293. Zbl0727.11033MR1058473
  6. [L] M. Laca, Semigroups of * -endomorphisms, Dirichlet series and Phase Transitions, J. Functional Analysis, to appear. Zbl0957.46039MR1608003
  7. [LR1] M. Laca and I. Raeburn, Semigroup crossed products and the Toeplitz algebras of non-abelian groups, J. Functional Analysis139 (1996), 415-440. Zbl0887.46040MR1402771
  8. [LR2] M. Laca and I. Raeburn, A semigroup crossed product arising in number theory, J. London Math. Soc., to appear. Zbl0922.46058MR1688505
  9. [Lg] S. Lang, Algebraic Number Theory, Second Edition, Springer-Verlag, BerlinHeidelbergNew YorkTokyo, 1994. Zbl0811.11001MR1282723
  10. [N] J. Neukirch, Class Field Theory, Grund. der math. Wissen. 280, Springer-Verlag, BerlinHeidelbergNew YorkTokyo, 1980. Zbl0587.12001MR819231
  11. [Ni] A. Nica, C* - algebras generated by isometries and Wiener-Hopf operators, J. Operator Theory27 (1992), 17-52. Zbl0809.46058MR1241114

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