Local norm convergence of states on the zero time Bose fields
HTML articles powered by AMS MathViewer
- by Ola Bratteli PDF
- Trans. Amer. Math. Soc. 188 (1974), 269-280 Request permission
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
- Huzihiro Araki, Type of von Neumann algebra associated with free field, Progr. Theoret. Phys. 32 (1964), 956–965. MR 180151, DOI 10.1143/PTP.32.956 F. Dixmier, Les algèbres d’opérateurs dans l’espace Hilbertien, Gauthier-Villars, Paris, 1969.
- James Glimm and Arthur Jaffe, The $\lambda (\phi ^{4})_{2}$ quantum field theory without cutoffs. III. The physical vacuum, Acta Math. 125 (1970), 203–267. MR 269234, DOI 10.1007/BF02392335
- 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
- A. Guichardet, Produits tensoriels infinis et représentations des relations d’anticommutation, Ann. Sci. École Norm. Sup. (3) 83 (1966), 1–52 (French). MR 0205097, DOI 10.24033/asens.1146 T. Spencer, Perturbation of the $P{(\phi )_2}$ quantum field Hamiltonian, J. Math. Phys. (1973).
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 188 (1974), 269-280
- MSC: Primary 81.46
- DOI: https://doi.org/10.1090/S0002-9947-1974-0342081-9
- MathSciNet review: 0342081