Related papers: Anomaly-free representations of the holonomy-flux …
On a closed and connected symplectic manifold, the group of Hamiltonian diffeomorphisms has the structure of an infinite-dimensional Fr\'echet Lie group, where the Lie algebra is naturally identified with the space of smooth and zero-mean…
We study the structure of operator algebras associated with the foliations which have projectively invariant measures. When a certain ergodicity condition on the measure preserving holonomies holds, the lack of holonomy invariant transverse…
Let $ N \in \mathbb{N} $, $ N \geq 2 $, be given. Motivated by wavelet analysis, we consider a class of normal representations of the $ C^* $-algebra $ \mathfrak{A}_{N} $ on two unitary generators $ U $, $ V $ subject to the relation \[…
This is a first study of the cosmology of classical fractional gravity, a nonlocal proposal endowed with self-adjoint fractional d'Alembertian operators which serves as the basis for an ultraviolet-complete theory of quantum gravity. We…
In orbifold gauge theory and gauge-Higgs unification models, gauge anomaly flows with an Aharonov-Bohm phase $\theta_H$ in the fifth dimension. We analyze $SU(2)$ gauge theory with doublet fermions in the flat $M^4 \times (S^1/Z_2)$…
Some features of extended loops are considered. In particular, the behaviour under diffeomorphism transformations of the wavefunctions with support on the extended loop space are studied. The basis of a method to obtain analytical…
We study gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since this model has local degrees of freedom, one has to face ``the problem of dynamics'', that is, diffeomorphism and Hamiltonian…
In Rovelli and Smolin's loop representation of nonperturbative quantum gravity in 4 dimensions, there is a space of solutions to the Hamiltonian constraint having as a basis isotopy classes of links in R^3. The physically correct inner…
Quantum general relativity may be considered as generally covariant QFT on differentiable manifolds, without any a priori metric structure. The kinematically covariance group acts by general diffeomorphisms on the manifold and by…
We revisit the covariant phase space formalism applied to gravitational theories with null boundaries, utilizing the most general boundary conditions consistent with a fixed null normal. To fix the ambiguity inherent in the Wald-Zoupas…
We present a group of transformations in the quantum configuration space of loop quantum gravity that contains the set of all transformations generated by the flux variables.
We show how extended topological quantum field theories (TQFTs) can be used to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert space together with a representation of the observable algebra including operators of…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like,…
We find robust obstructions to representing a Hamiltonian diffeomorphism as a full $k$-th power, $k \geq 2,$ and in particular, to including it into a one-parameter subgroup. The robustness is understood in the sense of Hofer's metric. Our…
To understand the underlying degrees of freedom, near horizon symmetry analysis of a black has gain significant interest in the recent past. In this paper we generalized those analysis first by taking into account a generic null surface…
We study real analytic perturbations of hyperbolic linear automorphisms on the 2-torus. The Koopman and the transfer operator are nuclear of order 0 when acting on a suitable Hilbert space. We show the generic existence of non-trivial…
We study the dynamics of strongly interacting gauge-theory matter (modelling quark-gluon plasma) in a boost-invariant setting using the AdS/CFT correspondence. Using Fefferman-Graham coordinates and with the help of holographic…
By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…
In this work the algebra of charges of diffeomorphisms at the horizon of generic black holes is analyzed within first order gravity. This algebra reproduces the algebra of diffeomorphisms at the horizon, (Diff(S^1)), without central…