General Relativity and Gravitation

, Volume 9, Issue 2, pp 101–121 | Cite as

The problem of scalar field theory in curved space-time

  • Mario Castagnino
Research Articles

Abstract

It is demonstrated that (1) there exist infiniteG1 that satisfy Lichnerowicz's conditions (L conditions) in a globally hyperbolic manifold; and, (2) there is noG1 in an expanding universe that would satisfy those conditions and that would behave as the ordinary Δ1 of flat space whenx → x′. The author thinks that these results present a serious problem for finding a semiclassical theory of scalar field in curved space-time.

Keywords

Manifold Field Theory Scalar Field Differential Geometry Hyperbolic Manifold 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Mario Castagnino
    • 1
  1. 1.Mathematics Department, Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de Buenos AiresBuenos AiresArgentina

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