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Some people and some problems met in half a century of commitment to mathematical physics

Abstract.

Personnal recollection of half a century of Mathematical Physics.

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References

  1. 1.

    Araki, Huzihiro, Rudolf Haag and Bert Schroer. 1961. The determination of a local or almost local field from a given current. Nuovo Cim. 19 (1): 90-102

    MATH  Article  Google Scholar 

  2. 2.

    Araki, Huzihiro. 1963a. A lattice of von Neumann algebras associated with the quantum theory of a free Bose field. J. Math. Phys. 4: 1343-1362

    MATH  Article  MathSciNet  ADS  Google Scholar 

  3. 3.

    Araki, Huzihiro and E.J. Woods. 1963b. Representations of the canonical commutation relations describing a nonrelativistic infinite free Bose gas. J. Math. Phys. 4: 637-662

    Article  MathSciNet  ADS  Google Scholar 

  4. 4.

    Araki, Huzihiro. 1964a. Von Neumann algebras of local observables for a free scalar field. J. Math. Phys. 5: 1-13

    MATH  Article  MathSciNet  ADS  Google Scholar 

  5. 5.

    Araki, Huzihiro. 1964b. Type of von Neumann algebras associated to the free field. Prog. Theoret. Phys. 32: 956-965

    MATH  Article  MathSciNet  ADS  Google Scholar 

  6. 6.

    Araki, Huzihiro and Rudolf Haag. 1967. Collision cross sections in terms of local observables. Commun. Math. Phys. 4: 77-91

    Article  ADS  Google Scholar 

  7. 7.

    Becchi, C., Rouet A. and Stora R.. 1975. Renormalization of the Abelian Higgs-Kibble model. Commun. Math. Phys. 42: 127-162

    Article  MathSciNet  ADS  Google Scholar 

  8. 8.

    Bekenstein, Jacob D. 1973. Black holes and entropy. Phys. Rev. D 7: 2333-2346

    Article  MathSciNet  ADS  Google Scholar 

  9. 9.

    Bell, John S. 1987. Speakable and Unspeakable in Quantum Mechanics. Cambridge Univ. Press

  10. 10.

    Bertlmann, R.A. and A. Zeilinger (Eds.). 2002. Quantum(Un)speakable. Springer

  11. 11.

    Bisognano, Joseph J. and Wichmann Eyvind H.. 1976. On the duality condition for quantum fields. J. Math. Phys. 17: 303-321

    Article  MathSciNet  ADS  Google Scholar 

  12. 12.

    Bopp, Fritz and Rudolf Haag. 1950. Über die Möglichkeit von Spinmodellen. Zs. Naturforsch. 5a: 644-653

    ADS  Google Scholar 

  13. 13.

    Bopp, Fritz. 1955. Würfelbrettspiele, deren Steine sich quantenmechanisch bewegen. Zs. Naturforsch. 10a: 9-10

    Google Scholar 

  14. 14.

    Borchers, Hans Jürgen, Rudolf Haag and Bert Schroer. 1963. The vacuum state in quantum field theory. Nuovo Cim. 29 (1): 148-162

    MATH  Article  Google Scholar 

  15. 15.

    Borchers, Hans Jürgen. 1965. Local rings and the connection of spin with statistics. Commun. Math. Phys. 1: 281-307

    MATH  Article  MathSciNet  ADS  Google Scholar 

  16. 16.

    Bratteli, Ola and Derek W. Robinson. 1979. Operator algebras and quantum statistical mechanics, Springer Heidelberg, New York

  17. 17.

    Brenig, Wilhelm and Rudolf Haag. 1959. Allgemeine Quantentheorie der Stossprozesse. Fortschr. Phys. 7: 183-242

    MATH  Article  Google Scholar 

  18. 18.

    Buchholz, Detley and Klaus Fredenhagen. 1982. Locality and the structure of particle states. Commun. Math. Phys. 84: 1-54

    MATH  Article  ADS  Google Scholar 

  19. 19.

    Buchholz, Detley and Wichmann Eyvind H.. 1986. Causal independence and the energy-level density of states in local quantum field theory. Commun. Math. Phys. 106: 321-344

    Article  Google Scholar 

  20. 20.

    Buchholz, Detley, D’Antoni C. and Klaus Fredenhagen. 1987. The universal structure of local algebras. Commun. Math. Phys. 111: 123-135

    MATH  Article  ADS  Google Scholar 

  21. 21.

    Coester, Fritz and Rudolf Haag. 1960. Representation of States in a Field Theory with Canonical Variables. Phys. Rev. 117: 1137-1145

    Article  MathSciNet  ADS  Google Scholar 

  22. 22.

    Coleman, Sidney and Jeffrey Mandula. 1967. All possible symmetries of the S-Matrix. Phys. Rev. 159: 1251-1256

    MATH  Article  ADS  Google Scholar 

  23. 23.

    Connes, Alain. 1973. Une classification des facteurs de type III. Ann. Sci. Ecole Norm. Sup. 6: 133-252

    MATH  MathSciNet  Google Scholar 

  24. 24.

    Dirac, P.A.M. 1938. Classical Theory of Radiating Electrons. Proc. R. Soc. Lond. A 167: 148-169

    Article  ADS  Google Scholar 

  25. 25.

    Doplicher, Sergio, Rudolf Haag and John E. Roberts. 1969a. Fields, observables and gauge transformations I. Commun. Math. Phys. 13: 1-23

    MATH  Article  ADS  Google Scholar 

  26. 26.

    Doplicher, Sergio, Rudolf Haag and Roberts John E.. 1969b. Fields, observables and gauge transformations II. Commun. Math. Phys. 15: 173-200

    MATH  Article  ADS  Google Scholar 

  27. 27.

    Doplicher, Sergio, Rudolf Haag and Roberts John E.. 1971. Local observables and particle statistics I. Commun. Math. Phys. 23: 199-230

    Article  ADS  Google Scholar 

  28. 28.

    Doplicher, Sergio, Rudolf Haag and Roberts John E.. 1974. Local observables and particle statistics II. Commun. Math. Phys. 35: 49-85

    Article  ADS  Google Scholar 

  29. 29.

    Doplicher, Sergio and Roberts John E.. 1989. Monoidal C*-categories and a new duality theory for compact groups. Invent. Math. 98: 157-218

    MATH  Article  MathSciNet  ADS  Google Scholar 

  30. 30.

    Doplicher, Sergio and Roberts John E.. 1990. Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics. Commun. Math. Phys. 131: 51-107

    MATH  Article  MathSciNet  ADS  Google Scholar 

  31. 31.

    Dürr, D., Goldstein S. and Zanghi N.. 1992. Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67: 843-907

    MATH  Article  ADS  Google Scholar 

  32. 32.

    Ekstein, H. 1956. Theory of timedependant scattering for multichannel processes. Phys. Rev. 101: 880-889

    MATH  Article  MathSciNet  ADS  Google Scholar 

  33. 33.

    Fell, J.M.G. 1960. The dual spaces of C*-algebras. Trans. Amer. Math. Soc. 94: 365-403

    MATH  MathSciNet  Google Scholar 

  34. 34.

    Fredenhagen, Klaus and Rudolf Haag. 1987. Generally covariant quantum field theory and scaling limits. Commun. Math. Phys. 108: 91-115

    MATH  Article  ADS  Google Scholar 

  35. 35.

    Fredenhagen, Klaus, Rehren K.H. and Bert Schroer. 1989. Superselection sectors with braid group statistics and exchange algebras I. General theory. Commun. Math. Phys. 125: 201-226

    MATH  Article  ADS  Google Scholar 

  36. 36.

    Fredenhagen, Klaus and Rudolf Haag. 1990. On the Derivation of Hawking Radiation Associated with the Formation of a Black Hole. Commun. Math. Phys. 127: 273-284

    MATH  Article  ADS  Google Scholar 

  37. 37.

    Friedrichs, K.O. 1953. Mathematical Aspects of the Quantum Theory of Fields. Commun. Pure Appl. Math. 6: 1-72

    MATH  Article  MathSciNet  Google Scholar 

  38. 38.

    Gårding, L. and Arthur S. Wightman. 1954a. Representations of the anticommutation relations. Proc. Nat. Acad. Sci. 40: 617-621

    MATH  Article  MathSciNet  Google Scholar 

  39. 39.

    Gårding, L. and Arthur S. Wightman. 1954b. Representations of the commutation relations. Proc. Nat. Acad. Sci. 40: 622-626

    MATH  Article  MathSciNet  Google Scholar 

  40. 40.

    Glaser, Yurko and Källén G.. 1956. A model of an unstable particle. Nucl. Phys. 2 (6): 706-722

    Google Scholar 

  41. 41.

    Green, H.S. 1953. A generalized method of field quantization. Phys. Rev. 90: 270-273

    MATH  Article  ADS  Google Scholar 

  42. 42.

    Haag, Rudolf. 1952. Der kanonische Formalismus in entarteten Fällen. Zamm 32 (7): 197-202

    MATH  Article  MathSciNet  Google Scholar 

  43. 43.

    Haag, Rudolf. 1954. Lecture Notes Copenhagen CERNT/RH1 53/54

  44. 44.

    Haag, Rudolf. 1955a. On Quantum Field Theories. DAN Mat. Fys. Medd. 29 (12)

  45. 45.

    Haag, Rudolf. 1955b. Die Selbstwechselwirkung des Elektrons. Zs. Naturforsch. 10a: 752-761

    ADS  Google Scholar 

  46. 46.

    Haag, Rudolf. 1958. Quantum Field Theories with Composite Particles and Asymptotic Conditions. Phys. Rev. 112: 669-673

    MATH  Article  MathSciNet  ADS  Google Scholar 

  47. 47.

    Haag, Rudolf. 1959. Discussion des « axioms » et des propriétés asymptotiques d’une théorie des champs locale avec particules composées, In: Les problèmes mathématique de la Théorie quantique des champs (Lille 1957). Centre Nationale de la Recherche Scientifique, Paris

  48. 48.

    Haag, Rudolf and Bert Schroer. 1962a. The postulates of quantum field theory. J. Math. Phys. 3: 248-256

    MATH  Article  ADS  Google Scholar 

  49. 49.

    Haag, Rudolf. 1962b. The mathematical structure of the Bardeen-Cooper-Schrieffer model. Nuovo Cim. 25 (2): 287-299

    MATH  Article  MathSciNet  Google Scholar 

  50. 50.

    Haag, Rudolf and Daniel Kastler. 1964. An algebraic approach to quantum field theory. J. Math. Phys. 5: 848-861

    MATH  Article  ADS  Google Scholar 

  51. 51.

    Haag, Rudolf and Swieca J. André. 1965. When does a quantum field theory describe particles? Commun. Math. Phys. 1: 308-320

    MATH  Article  MathSciNet  ADS  Google Scholar 

  52. 52.

    Haag, Rudolf, Nico M. Hugenholtz and Marinus Winnink. 1967. On the equilibrium states in quantum statistical mechanics. Commun. Math. Phys. 5: 215-236

    MATH  Article  ADS  Google Scholar 

  53. 53.

    Haag, Rudolf, Daniel Kastler and Trych-Pohlmeyer Ewa B.. 1974. Stability and equilibrium state. Commun. Math. Phys. 38: 173-193

    Article  ADS  Google Scholar 

  54. 54.

    Haag, Rudolf, Lopuszanski Jan T. and Martin Sohnius. 1975. All possible generators of supersymmetries of the S-Matrix. Nucl. Phys. B 88: 257-274

    Article  ADS  Google Scholar 

  55. 55.

    Haag, Rudolf, and Trych-Pohlmeyer Ewa B.. 1977. Stability properties of equilibrium states. Commun. Math. Phys. 56: 213-224

    Article  MathSciNet  ADS  Google Scholar 

  56. 56.

    Haag, Rudolf, Heide Narnhofer and Ulrich Stein. 1984. On quantum field theories in gravitational background. Commun. Math. Phys. 94: 219-238

    Article  ADS  Google Scholar 

  57. 57.

    Haag, Rudolf. 1990. Fundamental irreversibility and the concept of events. Commun. Math. Phys. 132: 245-251

    MATH  Article  MathSciNet  ADS  Google Scholar 

  58. 58.

    Haag, Rudolf and I. Ojima. 1995. On the problem of defining a specific theory within the frame of local quantum Physics. RIMS-1052 preprint, Kyoto University

  59. 59.

    Haag, Rudolf. 1996. An Evolutionary Picture for Quantum Physics. Commun. Math. Phys. 180: 733-743

    MATH  Article  MathSciNet  ADS  Google Scholar 

  60. 60.

    Haag, Rudolf. 1998. Objects, Events and Localization. ESI preprint 541: 1-23

    Google Scholar 

  61. 61.

    Haag, Rudolf. 1999. Quantentheorie und die Teilung der Welt, Z. Naturforsch. 54 (1): 2-10

    MathSciNet  Google Scholar 

  62. 62.

    Haag, Rudolf. 2001. Quantum Physics and Reality, Z. Naturforsch. 56a: 76-82

    Google Scholar 

  63. 63.

    Haag, Rudolf. 2004. Quantum Theory and the division of the World (revised translation). Mind and Matter 2 (2): 53-66

    Google Scholar 

  64. 64.

    Haag, Rudolf. 2010. Discussion of the ‘axioms’ and the asymptotic properties of a local field theory with composite particles. Eur. Phys. J. H 35 (3) 243-253 DOI: 10.1140/epjh/e2010-10041-3

    Article  Google Scholar 

  65. 65.

    Hawking, Steven W. 1975. Particle creation by black holes. Commun. Math. Phys. 43: 199-220

    Article  MathSciNet  ADS  Google Scholar 

  66. 66.

    Heisenberg, Werner. 1961. Lee model and quantisation of non linear field equations. Nucl. Phys. 4: 532-563

    Google Scholar 

  67. 67.

    Hund, Friedrich. 1961. Symmetriecharaktere von Termen bei Systemen mit gleichen Partikeln in der Quantenmechanik. Z. Phys. 43: 788-804

    ADS  Google Scholar 

  68. 68.

    Hund, Friedrich. 1961. Handbuch der Physik, Vol. XXIV, 2nd edn. Springer, Berlin

  69. 69.

    Jones, Vaughn F.R. 1961. Index for subfactors. Inventiones Mathematicae 72: 1-25

    Article  ADS  Google Scholar 

  70. 70.

    Kubo, Ryogo. 1961. Statistical mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn 12: 570-586

    Article  MathSciNet  ADS  Google Scholar 

  71. 71.

    Lehmann, Harry, Kurt Symanzik and Wolfhart Zimmermann. 1961. Zur Formulierung quantisierter Feldtheorien. Nuovo Cim. 1 (1): 205-225

    Article  Google Scholar 

  72. 72.

    Longo, R. 1961. Index of subfactors and statistics of quantum fields I. Invent. Math. 126: 217-247

    MathSciNet  Google Scholar 

  73. 73.

    Longo, R. 1961. Index of subfactors and statistics of quantum fields II: Correspondences, braid group statistics and Jones polynomial. Invent. Math. 130: 285-309

    MathSciNet  Google Scholar 

  74. 74.

    Martin, Paul C. and Julian Schwinger. 1961. Theory of many particle systems. I. Phys. Rev. 115: 1342-1373

    Article  ADS  Google Scholar 

  75. 75.

    Nishijima, Kazuhiko. 1961. Formulation of Field Theories of Composite Particles. Phys. Rev. 111: 995-1011

    Article  MathSciNet  ADS  Google Scholar 

  76. 76.

    Pusz, W. and Woronowicz S.L. 1961. Passive states and KMS-states for general quantum systems. Commun. Math. Phys. 58: 273-290

    Article  MathSciNet  ADS  Google Scholar 

  77. 77.

    Rehren, Karl-Henning. 1961. Field Operators for anyons and plektons. Commun. Math. Phys. 145: 123-148

    Article  MathSciNet  ADS  Google Scholar 

  78. 78.

    Rehren, K.H. 1961. On the range of the index of subfactors. J. Funct. Anal. 134: 183-193

    Article  MathSciNet  Google Scholar 

  79. 79.

    Rindler, W. 1961. Kruskal space and the uniformly accelerated frame. Am. J. Phys. 34: 1174-1178

    Article  MathSciNet  ADS  Google Scholar 

  80. 80.

    Rohrlich, Fritz T. 1961. Classical charged particles. Adison-Wesley Publ., Reading, Massachusetts

  81. 81.

    Ruelle, David. 1961. On the Asymptotic Condition in Quantum Field Theory. Helv. Phys. Acta 35: 147-163

    MathSciNet  Google Scholar 

  82. 82.

    Schroer, Bert. 1961. Infrateilchen in der Quantenfeldtheorie. Fortsch. Phys. 1: 1-31

    MathSciNet  Google Scholar 

  83. 83.

    Stapp, Henry Pierce. 1961. Theory of Reality. Found. Phys. 7: 313-323

  84. 84.

    Stapp, Henry Pierce. 1961. Whiteheadian Approach to Quantum theory and Generalized Bell’s Theorem. Found. Phys. 9: 1-25

    Article  MathSciNet  ADS  Google Scholar 

  85. 85.

    Takesaki, Masamichi. 1961. Tomita’s theory of modular Hilbert algebras and its application. Lecture Notes in Mathematics, Vol. 2. Springer-Verlag, Berlin

  86. 86.

    Unruh, W.G. 1961. Notes on black hole evaporation. Phys. Rev. D 14: 870-892

    Article  ADS  Google Scholar 

  87. 87.

    von Neumann, J. 1961. On infinite direct product. Comp. Math. 6: 1-77

    MathSciNet  Google Scholar 

  88. 88.

    Weizsäcker, Karl Friedrich von. 1961. Probability and Quantum Mechanics. Brit. J. Phil. Set. 24, 321-337

    Article  Google Scholar 

  89. 89.

    Whitehead, A.N. 1961. Process and Reality. An Essay in Cosmology. Mcmillan Publ. Co. Inc.

  90. 90.

    Wick, J.C. , Arthur S. Wightman and Eugene P. Wigner. 1961. The intrinsic parity of elementary particles. Phys. Rev. 88: 101-105

    Article  Google Scholar 

  91. 91.

    Wigner, Eugene P. 1961. On unitary representations of the inhomogeneous Lorentz Group. Annals of Mathematics 40 (1): 149-204

    Article  MathSciNet  Google Scholar 

  92. 92.

    Wigner, Eugene. 1961. Remarks on the mind-body question. In: Symmetries and Reflections. Indiana Univ. Press, Bloomington

  93. 93.

    Zimmermann, Wolfhart. 1961. On the Bound State Problem in Quantum Field Theory. Nuovo Cim. 10 (4): 597-614

    Article  Google Scholar 

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Haag, R. Some people and some problems met in half a century of commitment to mathematical physics. EPJ H 35, 263–307 (2010). https://doi.org/10.1140/epjh/e2010-10032-4

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Keywords

  • Black Hole
  • Mathematical Physic
  • Local Observable
  • Superselection Rule
  • Wightman Function