Related papers: Geodesic multiplication as a tool for classical an…
So called "analogue models" use condensed matter systems (typically hydrodynamic) to set up an "effective metric" and to model curved-space quantum field theory in a physical system where all the microscopic degrees of freedom are well…
A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are…
Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
Tangles of loops which approximate an aspect of the Kerr-Newman black hole metrics at large scales compared to the Planck length are constructed. The physical aspect the tangles approximate is discussed. This construction may be useful in…
In a previous paper, we showed how to use the techniques of the group of loops to formulate the loop approach to gravity proposed by Mandelstam in the 1960's. Those techniques allow to overcome some of the difficulties that had been…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.
Classical geometry can be described either in terms of a metric tensor $g_{ab}(x)$ or in terms of the geodesic distance $\sigma^2(x,x')$. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
In seeking to arrive at a theory of ``quantum gravity'', one faces several choices among alternative approaches. I list some of these ``forks in the road'' and offer reasons for taking one alternative over the other. In particular, I…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
Experiments are beginning to probe the interaction of quantum particles with gravitational fields beyond the uniform-field regime. In non-relativistic quantum mechanics, the gravitational field in such experiments can be written as a…
Recent theoretical schemes for utilizing cavity QED models as quantum simulators are reviewed. By considering a quadrature representation for the fields, it is shown how Jahn-Teller models, effective Abelian or non-Abelian gauge potentials,…
The notion of anyonic Wick algebras is introduced and the corresponding second quantisation procedure is discussed. Applications to the physics of 2D anyonic matter are presented. In particular the existence of thermodynamics in the…
We propose a new polymerization scheme for scalar fields coupled to gravity. It has the advantage of being a (non-bijective) canonical transformation of the fields and therefore ensures the covariance of the theory. We study it in detail in…
The interactions inside the (bisemi)particles are envisaged from two points of view: The first approach, based on the reducible representations of algebraic bilinear semigroups, allows to describe explicitly the interactions between…