Related papers: On state sums, internalisation and unification

Models for deterministic quantum mechanics of Cartan-Randers type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to Cartan-Randers…

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…

This contribution is a review of the method of isomonodromic quantization of dimensionally reduced gravity. Our approach is based on the complete separation of variables in the isomonodromic sector of the model and the related ``two-time"…

We consider the relation between three different approaches to defining quantum states across several times and locations: the pseudo-density matrix (PDM), the process matrix, and the multiple-time state approaches. Previous studies have…

After reviewing various interpretations of structural realism, I adopt here a definition that allows both relations between things that are already individuated (which I call ``relations between things'') and relations that individuate…

It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…

We give an overview of the current issues in early universe cosmology and consider the potential resolution of these issues in an as yet nascent spin foam cosmology. The model is the Barrett-Crane Model for quantum gravity along with a…

The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…

I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…

Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…

Starting from the defining transformations of complex matrices for the $SO(4,R)$ group, we construct the fundamental representation and the tensor and spinor representations of the group $SO(4,R)$. Given the commutation relations for the…

We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…

We summarize basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms, and sharing a purely combinatorial and algebraic language, and a discrete geometric interpretation. We emphasize…

We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…

A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…

We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within $SU(2)$ quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering…

It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific…

Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…

We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime disappears, replacing it with a discrete approximation to the causal path space described as an object in a model category. One of…

There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm…