Extended diffeomorphism algebras and trajectories in jet space
Abstract
Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra DRO(N) be the extension of $diff(N)\oplus diff(1)$ by its four inequivalent Virasorolike cocycles. Here $diff(N)$ is the diffeomorphism algebra in $N$dimensional spacetime and $diff(1)$ describes reparametrizations of trajectories in the space of tensorvalued $p$jets. DRO(N) has a Fock module for each $p$ and each representation of $gl(N)$. Analogous representations for gauge algebras (higherdimensional KacMoody algebras) are also given. The reparametrization symmetry can be eliminated by a gauge fixing procedure, resulting in previously discovered modules. In this process, two DRO(N) cocycles transmute into anisotropic cocycles for $diff(N)$. Thus the Fock modules of toroidal Lie algebras and their derivation algebras are geometrically explained.
 Publication:

arXiv eprints
 Pub Date:
 October 1998
 DOI:
 10.48550/arXiv.mathph/9810003
 arXiv:
 arXiv:mathph/9810003
 Bibcode:
 1998math.ph..10003L
 Keywords:

 Mathematical Physics
 EPrint:
 Expressions for abelian charges corrected. Published version