Related papers: Topological Shape Theory
We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
This paper deals with the model companion of an endomorphism acting on a vector space, possibly with extra structure. Given a theory $T$ that $\varnothing$-defines an infinite $K$-vector space $\mathbb{V}$ in every model, we set $T_\theta…
This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…
We introduce and develop fine shape, which has a very simple definition and aims to supersede all previously known shape theories for metrizable spaces. The problem with known shape theories of metrizable spaces is illustrated by the…
The review is devoted to topological global aspects of quantal description. The treatment concentrates on quantizations of kinematical observables --- generalized positions and momenta. A broad class of quantum kinematics is rigorously…
We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular…
Theories based on General Relativity or Quantum Mechanics have taken a leading position in macroscopic and microscopic Physics, but fail when used in the other extremity. Thus, we try to establish a new structure of united theory based on…
We give different perspectives on the notion of shape for condensed anima. We prove that it recovers more classical notions of shape for topological spaces in the cases of all paracompact compactly generated spaces and all locally…
Classically the kinetic theory for a perfect gas has zero spatial number density correlation between separate points because the particles are independent. But the joint spatial and temporal correlation is non-zero (and easily calculable)…
Shape Dynamics is a formulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance. In this paper we explicitly construct Shape Dynamics for a torus universe in 2+1 dimensions through a…
This work sets the statistical affine shape theory in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical…
We construct a geometric framework for cosmological large-scale structure based on optimal transport theory and Wasserstein geometry. In this framework, Ricci curvature on the probability measure space $\mathcal{P}_2(M)$ is characterized by…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…
In this PhD thesis, we develop a new approach to classical gravity starting from Mach's principles and the idea that the local shape of spatial configurations is fundamental. This new theory, "shape dynamics", is equivalent to general…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
It is well known that there are various models of gravitation: the metrical Hilbert-Einstein theory, a wide class of intrinsically Lorentz-invariant tetrad theories (of course, generally-covariant in the space-time sense), and many gauge…
Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…
Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…