Related papers: On state sums, internalisation and unification

In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in…

Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…

We provide two independent systematic methods of performing $D$-dimensional physical-state sums in gauge theory and gravity in such a way so that spurious light-cone singularities are not introduced. A natural application is to generalized…

The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…

I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are introduced (following hep-th/0205268) to deal…

Bargmann invariants, a class of gauge-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the geometric structure of quantum mechanics. This survey offers a…

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new…

There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…

In an attempt to re-establish space-time as an essential frame for formulating quantum gravity - rather than an "emergent" one -, we find that exact invariance under scale transformations is an essential new ingredient for such a theory.…

In my Montreal lecture notes of 1988, it was suggested that the theory of linear quantum groups can be presented in the framework of the category of {\it quadratic algebras} (imagined as algebras of functions on "quantum linear spaces"),…

We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…

Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…

Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum…

The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional…

Unitarity is a pillar of quantum theory. Nevertheless, it is also a source of several of its conceptual problems. We note that in a world where measurements are relational, as is the case in gravitation, quantum mechanics exhibits a…

It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…

The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…

Spin foam models are a new approach to a formulation of quantum gravity which is fully background independent, non-perturbative, and covariant, in the spirit of path integral formulations of quantum field theory. In this thesis we describe…

In this paper we look at 3D lattice models that are generalizations of the state sum model used to define the Kuperberg invariant of 3-manifolds. The partition function is a scalar constructed as a tensor network where the building blocks…