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Extended diffeomorphism algebras and trajectories in jet space

T. A. Larsson
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Abstract

Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra DRO(N) be the extension of $diff(N)\oplus diff(1)$ by its four inequivalent Virasoro-like cocycles. Here $diff(N)$ is the diffeomorphism algebra in $N$-dimensional spacetime and $diff(1)$ describes reparametrizations of trajectories in the space of tensor-valued $p$-jets. DRO(N) has a Fock module for each $p$ and each representation of $gl(N)$. Analogous representations for gauge algebras (higher-dimensional Kac-Moody 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.

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T. A. Larsson. 2000-11-30. Extended diffeomorphism algebras and trajectories in jet space. https://arxiv.org/abs/math-ph/9810003

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