Related papers: Space-time dynamics from algebra representations

Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…

In the groupoid approach to noncommutative quantization of gravity, gravitational field is quantized in terms of a C*-algebra A of complex valued funcions on a groupoid G (with convolution as multiplication). In the noncommutative quantum…

Based on an identified quantum relativity symmetry the contraction of which gives the Newtonian approximation of Galilean relativity, a quantum model of the physical space can be formulated with the Newtonian space seen in a way as the…

Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry,…

A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central…

Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\U(2)$. In extension of Feynman propagators for particle…

A theory in which points, lines, areas and volumes are on on the same footing is investigated. All those geometric objects form a 16-dimensional manifold, called C-space, which generalizes spacetime. In such higher dimensional space…

Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics - the theory of gravity - derivable from general principles of inductive inference? Tentative answers are suggested…

We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…

We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically…

The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…

This paper surveys the recent advances in the interactions between symbolic dynamics and C*-algebras. We explain how conjugacies and orbit equivalences of both two-sided (invertible) and one-sided (noninvertible) symbolic systems may be…

I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential…

By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean…

The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…

General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…

We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…

In a recent publication the I showed how the geometric algebra ${G}_{4,1}$, the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null geodesics should be allowed. The same paper…

We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…