How small is the phase space in quantum field theory ?

Detlev Buchholz; Martin Porrmann

Annales de l'I.H.P. Physique théorique (1990)

  • Volume: 52, Issue: 3, page 237-257
  • ISSN: 0246-0211

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Buchholz, Detlev, and Porrmann, Martin. "How small is the phase space in quantum field theory ?." Annales de l'I.H.P. Physique théorique 52.3 (1990): 237-257. <http://eudml.org/doc/76484>.

@article{Buchholz1990,
author = {Buchholz, Detlev, Porrmann, Martin},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {compactness and nuclearity; trace-class operators; space of functionals of limited energy; localization in configuration space; size of the phase space in quantum field theory; free field theory of massive and massless scalar particles in four space-time dimensions},
language = {eng},
number = {3},
pages = {237-257},
publisher = {Gauthier-Villars},
title = {How small is the phase space in quantum field theory ?},
url = {http://eudml.org/doc/76484},
volume = {52},
year = {1990},
}

TY - JOUR
AU - Buchholz, Detlev
AU - Porrmann, Martin
TI - How small is the phase space in quantum field theory ?
JO - Annales de l'I.H.P. Physique théorique
PY - 1990
PB - Gauthier-Villars
VL - 52
IS - 3
SP - 237
EP - 257
LA - eng
KW - compactness and nuclearity; trace-class operators; space of functionals of limited energy; localization in configuration space; size of the phase space in quantum field theory; free field theory of massive and massless scalar particles in four space-time dimensions
UR - http://eudml.org/doc/76484
ER -

References

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  1. [1] R. Haag and J.A. Swieca, When Does a Quantum Field Theory Describe Particles? Commun. Math. Phys., Vol. 1, 1965, pp. 308-320. Zbl0149.23803MR197077
  2. [2] D. Buchholz and E.H. Wichmann, Causal Independence and the Energy-Level Density of States in Local Quantum Field Theory, Commun. Math. Phys., Vol. 106, 1986, pp. 321-344. Zbl0626.46064MR855315
  3. [3] D. Buchholz, C. D'Antoni and R. Longo, Nuclear Maps and Modular Structures II: Applications to Quantum Field Theory (to appear in Commun. Math. Phys.). Zbl0773.47007MR1046280
  4. [4] K. Fredenhagen and J. Hertel, Unpublished manuscript, 1979. 
  5. Cf. also: R. Haag, Local Relativistic Quantum Physics, Physica, Vol. 124 A, 1984, pp. 357-364. MR759190
  6. [5] H. Jarchow, Locally Convex Spaces, Stuttgart: Teubner1981, Chapter 18. Zbl0466.46001MR632257
  7. [6] R. Wanzenberg, Energie und Präparierbarkeit von Zuständen in der lokalen Quantenfeldtheorie, Diplomarbeit, Hamburg, 1987. 
  8. [7] S. Doplicher and R. Longo, Standard and Split Inclusions of von Neumann Algebras, Invent. Math., Vol. 75, 1984, pp. 493-536. Zbl0539.46043MR735338
  9. [8] C. D'Antoni, S. Doplicher, K. Fredenhagen and R. Longo, Convergence of Local Charges and Continuity Properties of W*-Inclusions, Commun. Math. Phys., Vol. 110, 1987, pp. 325-348. Zbl0657.46045MR888004
  10. [9] J. Glimm and A. Jaffe, The λ(φ4)2 Quantum Field Theory Without Cutoffs, III. The physical vacuum, Acta Math., Vol. 125, 1970, pp. 203-267. MR269234
  11. [10] M. Porrmann, Ein verschärftes Nuklearitätskriterium in der lokalen Quantenfeldtheorie, Diplomarbeit, Hamburg, 1988. 
  12. [11] H. Araki, A Lattice of von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field, J. Math. Phys., Vol. 4, 1963, pp. 1343-1362. Zbl0132.43805MR158666
  13. [12] D. Buchholz and P. Jacobi, On the Nuclearity Condition for Massless Fields, Lett. Math. Phys., Vol. 13, 1987, pp. 313-323. Zbl0637.46079MR895294
  14. [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Fourier Analysis, Self-Adjointness, New York-San Francisco-London, Academic Press, 1975. Zbl0308.47002MR493420
  15. [14] M. Takesaki, Theory of Operator Algebras I, New York-Heidelberg-Berlin, Springer–Verlag, 1979. Zbl0436.46043MR1873025
  16. [15] D. Buchholz, C. D'Antoni and K. Fredenhagen, The Universal Structure of Local Algebras, Commun. Math. Phys., Vol. 111, 1987, pp. 123-135. Zbl0645.46048MR896763
  17. [16] D. Buchholz and P. Junglas, On the Existence of Equilibrium States in Local Quantum Field Theory, Commun. Math. Phys., Vol. 121, 1989, pp. 255-270. Zbl0673.46045MR985398
  18. [17] K. Fredenhagen and J. Hertel, Local Algebras of Observables and Pointlike Localized Fields, Commun. Math. Phys., Vol. 80, 1981, pp. 555-561. Zbl0472.46051MR628511
  19. [18] J. Rehberg and M. Wollenberg, Quantum Fields as Pointlike Localized Objects, Math. Nachr., Vol. 125, 1986, pp. 259-274. Zbl0617.46080MR847366
  20. [19] R. Haag and B. Schroer, Postulates of Quantum Field Theory, J. Math. Phys., Vol. 3, 1962, pp. 248-256. Zbl0125.21903MR138387
  21. [20] D. Buchholz, On Particles, Infraparticles, and the Problem of Asymptotic Completeness, In VIIIth International Congress on Mathematical Physics, Marseille, 1986. Singapore : World Scientific, 1987. MR915584
  22. [21] H.J. Borchers, R. Haag and B. Schroer, The Vacuum State in Quantum Field Theory, Nuovo Cimento, Vol. 29, 1963, pp. 148-162. Zbl0133.23301MR154607

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