Covariant Formulation of Classical Gravity
Apr, 1990
24 pages
Published in:
- Nucl.Phys.B 349 (1991) 791-814
- Published: 1991
Report number:
- ITP-SB-90-26
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Abstract: (Elsevier)
A covariant formulation of the recently discovered gauge theory for W 3 -type algebras is presented. It is obtained by a systematic construction, which starts from the classical (Poisson) W 3 -algebra. Having associated to each annihilation generator a gauge field and local parameter, and to each creation generator a field in the coadjoint representation, we require that all curvatures vanish and we adopt gauge choices which are such that only a finite number of gauge fields remain: the vielbeins e μ ± and W-vielbeins B μ ++ , B μ −− , corresponding to the gauge parameters k ± (diffeomorphisms) and λ ±± (W-gravity). Apart from these the gauge sector has manifest local Weyl, Lorentz and “W-Weyl” and “W-Lorentz” symmetries. Matter is coupled by introducing an infinite set of scalar fields subject to a constraint which leaves only one physical field. This constraint is in turn identified with a field equation and yields upon integration, using an integrating factor, an invariant action. Various gauge choices are discussed.- gravitation
- dimension: 2
- gauge field theory: W(3)
- invariance: Lorentz
- algebra: representation
- field theory: action
- field equations
- coupling: matter
- matter: coupling
- dependence: gauge
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