Related papers: Finitary Algebraic Superspace
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
We give an expanded discussion of the proposal that spacetime supersymmetry representations may be viewed as having their origins in 1D theories that involve a special class of real Clifford algebras. These 1D theories reproduce the…
An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent…
The paper reviews the most illustrative cases of the "peculiar/anomalous" experiences of time (and, to a lesser extent, also space) and discusses a simple algebraic geometrical model accounting for the most pronounced of them.
As a novel approach with possible relevance to semiclassical gravity, we propose to define regions of space as quantum subsystems. After recalling how to divide a generic quantum system into ``parts'', we apply this idea to a free scalar…
We assume that space-time at the Planck scale is discrete, quantised in Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that is, quantum space-time can be viewed as a quantum computer. Within this model, one finds…
By virtue of harmonic maps on two-dimensional spheres (S$^{2}$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and…
We study a model of scalar quantum field theory in which space-time is a discrete set of points obtained by repeatedly subdividing a triangle into three triangles at the centroid. By integrating out the field variable at the centroid we get…
By exploring a possible physical realisation of the geometric concept of noncommutative tangent bundle, we outline an axiomatic quantum picture of space as topological manifold and time as a count of its reconfiguration events.
In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
The progress brought to the study of chiral fermions and gauge theories by quantization methods with a bulk time suggests their usefulness in supersymmetric theories. Using superspace methods, we show how an explicitly supersymmetric…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
A recently proposed algebraic representation of the causal set model of the small-scale structure of space-time of Sorkin et al. is briefly reviewed and expanded. The algebraic model suggested, called quantum causal set, is physically…
The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in a non-spatial degree of freedom, can greatly simplify the…
Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…