How small is the phase space in quantum field theory ?
Annales de l'I.H.P. Physique théorique, Tome 52 (1990) no. 3, pp. 237-257. 
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     author = {Buchholz, Detlev and Porrmann, Martin},
     title = {How small is the phase space in quantum field theory ?},
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     volume = {52},
     number = {3},
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     zbl = {0719.46044},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1990__52_3_237_0/}
}
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Buchholz, Detlev; Porrmann, Martin. How small is the phase space in quantum field theory ?. Annales de l'I.H.P. Physique théorique, Tome 52 (1990) no. 3, pp. 237-257. http://www.numdam.org/item/AIHPA_1990__52_3_237_0/

[1] R. Haag and J.A. Swieca, When Does a Quantum Field Theory Describe Particles? Commun. Math. Phys., Vol. 1, 1965, pp. 308-320. | MR | Zbl

[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. | MR | Zbl

[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.). | MR | Zbl

[4] K. Fredenhagen and J. Hertel, Unpublished manuscript, 1979.

Cf. also: R. Haag, Local Relativistic Quantum Physics, Physica, Vol. 124 A, 1984, pp. 357-364. | MR

[5] H. Jarchow, Locally Convex Spaces, Stuttgart: Teubner 1981, Chapter 18. | MR | Zbl

[6] R. Wanzenberg, Energie und Präparierbarkeit von Zuständen in der lokalen Quantenfeldtheorie, Diplomarbeit, Hamburg, 1987.

[7] S. Doplicher and R. Longo, Standard and Split Inclusions of von Neumann Algebras, Invent. Math., Vol. 75, 1984, pp. 493-536. | MR | Zbl

[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. | MR | Zbl

[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. | MR

[10] M. Porrmann, Ein verschärftes Nuklearitätskriterium in der lokalen Quantenfeldtheorie, Diplomarbeit, Hamburg, 1988.

[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. | MR | Zbl

[12] D. Buchholz and P. Jacobi, On the Nuclearity Condition for Massless Fields, Lett. Math. Phys., Vol. 13, 1987, pp. 313-323. | MR | Zbl

[13] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Fourier Analysis, Self-Adjointness, New York-San Francisco-London, Academic Press, 1975. | MR | Zbl

[14] M. Takesaki, Theory of Operator Algebras I, New York-Heidelberg-Berlin, Springer-Verlag, 1979. | MR | Zbl

[15] D. Buchholz, C. D'Antoni and K. Fredenhagen, The Universal Structure of Local Algebras, Commun. Math. Phys., Vol. 111, 1987, pp. 123-135. | MR | Zbl

[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. | MR | Zbl

[17] K. Fredenhagen and J. Hertel, Local Algebras of Observables and Pointlike Localized Fields, Commun. Math. Phys., Vol. 80, 1981, pp. 555-561. | MR | Zbl

[18] J. Rehberg and M. Wollenberg, Quantum Fields as Pointlike Localized Objects, Math. Nachr., Vol. 125, 1986, pp. 259-274. | MR | Zbl

[19] R. Haag and B. Schroer, Postulates of Quantum Field Theory, J. Math. Phys., Vol. 3, 1962, pp. 248-256. | MR | Zbl

[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. | MR

[21] H.J. Borchers, R. Haag and B. Schroer, The Vacuum State in Quantum Field Theory, Nuovo Cimento, Vol. 29, 1963, pp. 148-162. | MR | Zbl