Abstract
We propose a generalization of the Haag-Kastler axioms for local observables to Lorentzian manifolds. The framework is intended to resolve ambiguities in the construction of quantum field theories on manifolds. As an example we study linear scalar fields for globally hyperbolic manifolds.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fourés-Bruhat, Y.: Propagateurs et solutions d'equations homogénes hyperboliques. C. R. Acad. Sci.251, 29 (1960)
Choquet-Bruhat, Y.: Hyperbolic differential equations on a manifold. In: Batelle rencontres (eds. C. De Witt, J. Wheeler). New York: Benjamin 1977
De Witt, B.: Quantum field theory in curved space-time. Phys. Rep. 19C 295 (1974)
Dimock, J.: Scalar quantum field in an external gravitational field. J. Math. Phys. (N. Y.)20, 2549 (1979)
Dyson, F.: Missed opportunities. Bull. Am. Math. Soc.78, 635 (1972)
Geroch, R.: The domain of dependence. J. Math. Phys. (N. Y.)11, 437 (1970)
Guillemin, V., Sternberg, S.: Geometric asymptotics, Providence, R.I.: Amer. Math. Soc. 1977
Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 848 (1964)
Haag, R., Schroer, S.: Postulates of quantum field theory, J. Math. Phys.3, 248 (1962)
Hajicek, P.: Observables for quantum fields on curved backgrounds. In: Differential geometrical methods in mathematical physics II (eds. K. Bleuler, H. Petry, A. Reetz), p. 535. Berlin, Heidelberg, New York: Springer 1978
Hawking, S., Ellis, G.: The large scale structure of space-time. Cambridge: Cambridge University Press, 1973
Isham, C.: Quantum field theory in curved space-time: a general mathematical framework. In: Differential geometrical methods in mathematical physics II (eds. K. Bleuler, H. Petry, A. Reetz), p. 459. Berlin, Heidelberg, New York: Springer 1978
Kay, B.: Linear spin-zero quantum fields in external gravitational and scalar fields: I: Commun. Math. Phys.62, 55 (1978); II: Commun. Math. Phys.71, 29, (1980)
Leray, J.: Hyperbolic differential equations. Lecture notes, Princeton 1953 (unpublished)
Lichnerowicz, A.: Propagateurs et commutateurs en relativité général. Publication IHES, no. 10, (1961)
Penrose, R.: Techniques of differential topology in relativity. SIAM, Philadelphia (1972)
Simon, B.: Topics in functional analysis. In: Mathematics of contemporary physics (ed. R. Streater). New York: Academic Press 1972
Wald, R.: Existence of the S-matrix in quantum field theory in curved space-time. Ann. Phys. (N. Y.)118, 490 (1979)
Author information
Authors and Affiliations
Additional information
Communicated by R. Haag
Supported by National Science Foundation PHY 77-21740.
On leave from Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14214, USA
Rights and permissions
About this article
Cite this article
Dimock, J. Algebras of local observables on a manifold. Commun.Math. Phys. 77, 219–228 (1980). https://doi.org/10.1007/BF01269921
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01269921