Fock representations of non-centrally extended super-diffeomorphism algebras

Lowest-energy representations of non-centrally extended diffeomorphism algebras

We describe a class of non-central extensions of the diffeomorphism algebra in N-dimensional spacetime, and construct lowest-energy modules thereof, thus generalizing work of Eswara-Rao and Moody. There is one representation for each representation of $Vir\ltimes_{k_0}\km{gl(N)}$ (an extension of the semi-direct product). Similar modules are constructed for gauge algebras.

Koszul-Tate Cohomology as Lowest-Energy Modules of Non-Centrally Extended Diffeomorphism Algebras

Fock modules for multi-dimensional Virasoro algebras (non-central extensions of the diffeomorphism algebra vect(N)) have recently been reported. Using ideas from the antifield formalism, I construct new classes of lowest-energy modules, as cohomology groups of a certain Fock complex. The Fock construction involves a passage to p-jets prior to normal ordering, but the abelian charges usually diverge in the limit p --> oo. The requirement of a finite limit imposes severe restrictions on the number of spacetime dimensions and on the order of the Euler-Lagrange (EL) equations. Under some natural a…

圈量子引力微分同胚不变Hilbert空间的Fock空间结构及其应用

A Fock space structure for the diffeomorphism invariant Hilbert space of loop quantum gravity and its applications

本文证明了圈量子引力微分同胚不变态空间在特定假设下具有Fock空间结构，借此将群场论凝聚态表示为LQG相干态，并探索了单/多粒子态的量子几何特征。

Extended diffeomorphism algebras and trajectories in jet space

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, resultin…

Multi-dimensional Diffeomorphism and Current Algebras from Virasoro and Kac-Moody Currents

The recently constructed Fock representations of $N$-dimensional diffeomorphism and current algebras are reformulated in terms of one-dimensional currents, satisfying Virasoro and affine Kac-Moody algebras.

Loop groups and diffeomorphism groups of the circle as colimits

We show that loop groups and the universal cover of $\mathrm{Diff}_+(S^1)$ can be expressed as colimits of groups of loops/diffeomorphisms supported in subintervals of $S^1$. Analogous results hold for based loop groups and for the based diffeomorphism group of $S^1$. These results continue to hold for the corresponding centrally extended groups. We use the above results to construct a comparison functor from the representations of a loop group conformal net to the representations of the corresponding affine Lie algebra. We also establish an equivalence of categories between solitonic represen…