Electronic Resource
Springer
Communications in mathematical physics
156 (1993), S. 245-275
ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case ofW ∞-gravity is analysed in detail. While the gauge group for gravity ind dimensions is the diffeomorphism group of the space-time, the gauge group for a certainW-gravity theory (which isW ∞-gravity in the cased=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations forW-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising $$\sqrt {\det g_{\mu \nu } }$$ ) only ifd=1 ord=2, so that only ford=1,2 can actions be constructed. These two cases and the correspondingW-gravity actions are considered in detail. Ind=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphism group. Some of the constraints that arise ford=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations ofW-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02098483
Permalink
Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |