相关论文: On the extended loop calculus

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…

The evaluation of loop amplitudes via differential equations and harmonic polylogarithms is discussed at an introductory level. The method is based on evolution equations in the masses or in the external kinematical invariants and on a…

We compute the one-loop quantum corrections to the interactions between the two metrics of the ghost-free massive bigravity. When considering gravitons running in the loops, we show how the structure of the interactions gets destabilized at…

Models of gravity in warped extra dimensions enjoy invariance under diffeomorphism. We derive the nonlinear transformation rules for the metric perturbations in the unitary gauge. As an off-shell symmetry, the main consequence of…

We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative…

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,…

In this article we continue the work on translating elements of the perturbative quantum field theory defined on Minkowski spacetime into the background independent framework of Loop Quantum Gravity. We present the construction of r-Fock…

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are…

After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…

The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…

This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…

We consider the extension of the Jackson calculus into higher dimensions and specifically into Clifford analysis.

New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…

We investigate all feasible mathematical representations of disformal transformations on a space-time metric according to the action of a linear operator upon the manifold's tangent and cotangent bundles. The geometric, algebraic and group…

The inertial and gravitational properties of intrinsic spin are discussed and some of the recent work in this area is briefly reviewed. The extension of relativistic wave equations to accelerated systems and gravitational fields is…

It has been pointed out that the holonomy of generic extended loops is not gauge covariant. We show how to define a family of extended loops for which previous criticism does not apply. We also give sufficient conditions that extended loops…

These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…

Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of…

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…