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Local quasiequivalence and adiabatic vacuum states. (English) Zbl 0749.46045
Summary: The problem of determining the physically relevant states acquires a new dimension in curved spacetime where there is, in general, no natural definition of a vacuum state. It is argued that there is a unique local quasiequivalence class of physically relevant states and it is shown how this class can be specified for the free Klein-Gordon field on a Robertson-Walker spacetime by using the concept of an adiabatic vacuum state. Any two adiabatic vacuum states of order two are locally quasiequivalent.

46N50 Applications of functional analysis in quantum physics
81T20 Quantum field theory on curved space or space-time backgrounds
Full Text: DOI
[1] Haag, R., Narnhofer, H., Stein, U.: On quantum field theory in gravitational background. Commun. Math. Phys.94, 219–238 (1984) · doi:10.1007/BF01209302
[2] Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 848–861 (1964). · Zbl 0139.46003 · doi:10.1063/1.1704187
[3] Dimock, J.: Algebras of local observables on a manifold. Commun. Math. Phys.77, 219–228 (1980) · Zbl 0455.58030 · doi:10.1007/BF01269921
[4] Araki, H., Yamagami, S.: On quasiequivalence of quasifree states of the canonical commutation relations. Publ. RIMS, Kyoto18, 283–338 (1982) · Zbl 0505.46052
[5] Najmi, A. H., Ottewill, A. C.: Quantum states and the Hadamard form. III. Constraints in cosmological space-times. Phys. Rev.D32, 1942–1948 (1985). · doi:10.1103/PhysRevD.32.1942
[6] Bernard, D.: Hadamard singularity and quantum states in Bianchi type-I space-time. Phys. Rev.D33, 3581–3589 (1986) · doi:10.1103/PhysRevD.33.3581
[7] Mazzitelli, F. D., Paz, J. P., Castagnino, M. A.: Cauchy data and Hadamard singularities in time-dependent backgrounds. Phys. Rev.D36, 2994–3001
[8] Fulling, S. A., Narcowich, F. J., Wald, R. M.: Singularity structure of the two-point function in quantum field theory in curved spacetime II. Ann. Phys.136, 243–272 (1981) · Zbl 0495.35054 · doi:10.1016/0003-4916(81)90098-1
[9] Kay, B. S.: Linear spin-zero quantum fields in external gravitational and scalar fields I. Commun. Math. Phys.62, 55–70 (1978) · doi:10.1007/BF01940330
[10] Gelfand, I. M., Graev, M. I., Vilenkin, N. J.: Generalized functions, vol. 5. New York, London: Academic Press 1966 · Zbl 0144.17202
[11] Vilenkin, N. J.: Special functions and the theory of group representations. Providence, Rhode Island: American Mathematical Society 1968 · Zbl 0172.18404
[12] Dixmier, J.:C *-Algebras. Amsterdam, New York, Oxford: North-Holland 1977 · Zbl 0372.46058
[13] Parker, L.: Quantized fields and particle creation in expanding universes I. Phys. Rev.183, 1057–1068 (1969) · Zbl 0186.58603 · doi:10.1103/PhysRev.183.1057
[14] Parker, L., Fulling, S. A.: Adiabatic regularization of the energy-momentum tensor of a quantized field in homogeneous spaces. Phys. Rev.D9, 341–354 (1974) · doi:10.1103/PhysRevD.9.341
[15] Buchholz, D.: Product states for local algebras. Commun. Math. Phys.36, 287–304 (1974) · Zbl 0289.46050 · doi:10.1007/BF01646201
[16] Hörmander, L.: The analysis of linear partial differential operators I. Berlin, Heidelberg, New York: Springer 1983 · Zbl 0521.35001
[17] Araki, H.: Von Neumann algebras of local observables for the free scalar field. J. Math. Phys.5, 1–13 (1964). · Zbl 0151.44401 · doi:10.1063/1.1704063
[18] Hörmander, L.: Linear partial differential operators. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0321.35001
[19] Trèves, F.: Basic linear partial differential equations. New York, San Francisco, London: Academic Press 1975 · Zbl 0305.35001
[20] Palais, R. S.: Seminar on the Atiyah-Singer index theorem. Princeton, New Jersey: Princeton University Press 1965 · Zbl 0137.17002
[21] Fell, J. M. G.: The dual spaces ofC *-algebras. Trans. Am. Math. Soc.94, 365–403 (1960) · Zbl 0090.32803
[22] Fell, J. M. G.: The structure of algebras of operator fields. Acta Math.106, 233–280 (1961) · Zbl 0101.09301 · doi:10.1007/BF02545788
[23] Stein, E. M.: Singular integrals and differentiability properties of functions. Princeton, New Jersey: Princeton University Press 1970 · Zbl 0207.13501
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