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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Local norm convergence of states on the zero time Bose fields

Author: Ola Bratteli
Journal: Trans. Amer. Math. Soc. 188 (1974), 269-280
MSC: Primary 81.46
MathSciNet review: 0342081
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Abstract: For a sequence of vector states on the Boson Fock space which are norm convergent on the Newton-Wigner local algebras, conditions are given which guarantee norm convergence on the relativistic local algebras also. These conditions are verified for the cutoff physical vacuum states of the $ P{(\phi )_2}$ field theory, and yield a simplification of the proof of the locally normal property of the physical vacuum in that theory.

References [Enhancements On Off] (What's this?)

  • [1] Huzihiro Araki, Type of von Neumann algebra associated with free field, Progr. Theoret. Phys. 32 (1964), 956–965. MR 0180151,
  • [2] F. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, Gauthier-Villars, Paris, 1969.
  • [3] James Glimm and Arthur Jaffe, The 𝜆(𝜙⁴)₂ quantum field theory without cutoffs. III. The physical vacuum, Acta Math. 125 (1970), 203–267. MR 0269234,
  • [4] J. Glimm and A. Jaffe, Boson quantum field models, Mathematics of contemporary physics (Proc. Instructional Conf. (NATO Advanced Study Inst.), Bedford Coll., London, 1971) Academic Press, New York, 1972, pp. 77–143. MR 0674511
  • [5] A. Guichardet, Produits tensoriels infinis et représentations des relations d’anticommutation, Ann. Sci. École Norm. Sup. (3) 83 (1966), 1–52 (French). MR 0205097
  • [6] T. Spencer, Perturbation of the $ P{(\phi )_2}$ quantum field Hamiltonian, J. Math. Phys. (1973).

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Keywords: Boson Fock space, $ P{(\phi )_2}$ theory, local algebras, locally normal states, annihilation and creation operators
Article copyright: © Copyright 1974 American Mathematical Society

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