Related papers: Gravity Formality
In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the…
We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be…
Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant…
This paper studies formal deformations and homotopy theory of Rota-Baxter algebras of any weight. We define an $L_\infty$-algebra, which controls simultaneous deformations of associative products and Rota-Baxter operators. As a consequence,…
In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, $n$-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level lift of a…
We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
A dg cyclic operad $BVHgraphs$ of hypergraphs is introduced which comes equipped with an explicit quasi-isomorphism $BV\rightarrow BVHgraphs$ from the { cyclic} operad $BV$ of Batalin-Vilkovisky algebras. A proof that the cohomology of…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements…
We construct a canonical chain of formality quasiisomorphisms for the operad of chains on framed little disks and the operad of chains on little disks. The construction is done in terms of logarithmic algebraic geometry and is remarkable…
We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on…
The goal of this article is to relate recent developments in cyclic homology theory with the theory of operads and homotopical algebra, and hence to provide a general framework to define and study operations in cyclic homology theory.
A brief review is given of an adaptation of the coadjoint orbit method appropriate for study of models with infinite-dimensional symmetry groups. It is illustrated on several examples, including derivation of the WZNW action of induced…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin$^c$-complex under consideration is allowed to be further twisted by certain natural exterior…
We generalize some of the standard homological techniques to $\cW$-algebras, and compute the semi-infinite cohomology of the $\cW_3$ algebra on a variety of modules. These computations provide physical states in $\cW_3$ gravity coupled to…
We study homotopy theory of the wheeled prop controlling Poisson structures on arbitrary formal graded finite-dimensional manifolds and prove, in particular, that Grothendieck-Teichmueller group acts on that wheeled prop faithfully and…
We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and…
Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite.…
A common approach in physics and mathematics is to extend and modify theories and frameworks by considering what is often described as a `natural' extension or modification by including higher-order terms or by introducing other…