Abstract
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.
Similar content being viewed by others
References
Haag, R., Narnhofer, H., Stein, U.: On quantum field theory in gravitational background. Commun. Math. Phys.94, 219–238 (1984)
Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 848–861 (1964).
Dimock, J.: Algebras of local observables on a manifold. Commun. Math. Phys.77, 219–228 (1980)
Araki, H., Yamagami, S.: On quasiequivalence of quasifree states of the canonical commutation relations. Publ. RIMS, Kyoto18, 283–338 (1982)
Najmi, A. H., Ottewill, A. C.: Quantum states and the Hadamard form. III. Constraints in cosmological space-times. Phys. Rev.D32, 1942–1948 (1985).
Bernard, D.: Hadamard singularity and quantum states in Bianchi type-I space-time. Phys. Rev.D33, 3581–3589 (1986)
Mazzitelli, F. D., Paz, J. P., Castagnino, M. A.: Cauchy data and Hadamard singularities in time-dependent backgrounds. Phys. Rev.D36, 2994–3001
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)
Kay, B. S.: Linear spin-zero quantum fields in external gravitational and scalar fields I. Commun. Math. Phys.62, 55–70 (1978)
Gelfand, I. M., Graev, M. I., Vilenkin, N. J.: Generalized functions, vol. 5. New York, London: Academic Press 1966
Vilenkin, N. J.: Special functions and the theory of group representations. Providence, Rhode Island: American Mathematical Society 1968
Dixmier, J.:C *-Algebras. Amsterdam, New York, Oxford: North-Holland 1977
Parker, L.: Quantized fields and particle creation in expanding universes I. Phys. Rev.183, 1057–1068 (1969)
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)
Buchholz, D.: Product states for local algebras. Commun. Math. Phys.36, 287–304 (1974)
Hörmander, L.: The analysis of linear partial differential operators I. Berlin, Heidelberg, New York: Springer 1983
Araki, H.: Von Neumann algebras of local observables for the free scalar field. J. Math. Phys.5, 1–13 (1964).
Hörmander, L.: Linear partial differential operators. Berlin, Heidelberg, New York: Springer 1976
Trèves, F.: Basic linear partial differential equations. New York, San Francisco, London: Academic Press 1975
Palais, R. S.: Seminar on the Atiyah-Singer index theorem. Princeton, New Jersey: Princeton University Press 1965
Fell, J. M. G.: The dual spaces ofC *-algebras. Trans. Am. Math. Soc.94, 365–403 (1960)
Fell, J. M. G.: The structure of algebras of operator fields. Acta Math.106, 233–280 (1961)
Stein, E. M.: Singular integrals and differentiability properties of functions. Princeton, New Jersey: Princeton University Press 1970
Author information
Authors and Affiliations
Additional information
Communicated by H. Araki
Rights and permissions
About this article
Cite this article
Lüders, C., Roberts, J.E. Local quasiequivalence and adiabatic vacuum states. Commun.Math. Phys. 134, 29–63 (1990). https://doi.org/10.1007/BF02102088
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02102088