theories on five-dimensional space-time

H.P. Künzle

Department of Mathematics, University of Alberta

Edmonton, Canada T6G 2G1*e-mail:*HP.Kunzle@UAlberta.ca

and

C. Duval

Centre de Physique Théorique

C.N.R.S. Luminy, Case 907

F 13288 Marseille Cedex 9, France

*e-mail:* Christian.Duval@cptsu5.univ-mrs.fr

**Abstract**

A five-dimensional Lorentzian manifold *(M,g)* together with a
covariantly constant vector field *X* has proved to be a
convenient framework in which to describe, in a unified way,
relativistic physical theories as well as their nonrelativistic
limits. If *X* is a space-like vector field the quotient manifold *X*} becomes the standard four-dimensional
general relativistic space-time, but if *X* is a nullvector the
corresponding quotient space inherits a full Newton-Cartan
structure. In this paper a survey of applications is presented which
include, apart from the Einsteinian and Newtonian gravitation
theory,
other classical field theories (Dirac field, perfect fluids,
Yang-Mills fields) as well as a some remarks about possible models of
a particle systems. For field theories one starts
with a five-dimensional Lagrangian similar in structure to the
standard relativistic one. The field equations and a stress-energy
tensor can be derived in a straightforward way. The additional
components of this tensor on five-dimensional space-time lead to some
interesting questions of interpretation.