Related papers: Constraint Algebra in Causal Loop Quantum Gravity

As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain non-linear Poisson brackets which are ``cocycle perturbations'' of the linear Poisson bracket. We show that these special Poisson…

There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition…

In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing method observables form a quotient Dirac bracket algebra. We show that these two algebras…

We study the deformation (Moyal) quantisation of gravity in both the ADM and the Ashtekar approach. It is shown, that both can be treated, but lead to anomalies. The anomaly in the case of Ashtekar variables, however, is merely a central…

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…

There exists the problem to construct a quantum algebra of observables in lightcone QCD beyond the perturbative regime. It has recently established that the boundary gauge fields are crucial for a consistent construction of the classical…

This paper is devoted to the analysis of massive particle in general and Newton-Cartan Background in de Broglie-Bohm Theory. We find classical and quantum version of Hamilton-Jacobi equations and find their relations to wave equations. We…

We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…

Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum…

This work introduces a new space $\T'_*$ of `vertex-smooth' states for use in the loop approach to quantum gravity. Such states provide a natural domain for Euclidean Hamiltonian constraint operators of the type introduced by Thiemann (and…

In treatments of electromagnetism, it is often tacitly assumed that the vector potentials of the field and their conjugate momenta satisfy the canonical Poisson bracket relations, despite the fact that the components of the vector potential…

We show that the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity can be non-trivially deformed by allowing the cosmological constant to become an arbitrary function of the (Weyl) curvature. Our result implies…

The spectrum of primordial perturbations obtained by calculating the quantum gravitational corrections to the dynamics of scalar perturbations is compared with Planck 2013 and BICEP2/{\it Keck Array} public data. The quantum gravitational…

In this essay we present evidence suggesting that loop quantum gravity leads to deformation of the local Poincar\'e algebra within the limit of high energies. This deformation is a consequence of quantum modification of effective off-shell…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a…

We consider the non-relativistic limit of general relativity coupled to a $(p+1)$-form gauge field and a scalar field in arbitrary dimensions and investigate under which conditions this gives rise to a Poisson equation for a Newton…

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…

Beginning from the Ashtekar formulation of canonical general relativity, we derive a physical Hamiltonian written in terms of (classical) loop gravity variables. This is done by gauge-fixing the gravitational fields within a complex of…

The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the…