Related papers: Non-Commutative Worlds and Classical Constraints
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity -- diffeomorphisms -- moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry…
We study the implications of a noncommutative geometry of the minisuperspace variables for the FRW universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution…
A reconciliation of gravitation and electromagnetism has eluded physics for neearly a century. It is argued here that this is because both quantum physics and classical physics are set in differentiable space time manifolds with point…
Scaling symmetries have previously been examined for classical field theories described by singular Lagrangians; in this article, we apply these results to the first-order formulation of General Relativity. It is shown that the dynamical…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
Following the line of the history, if by one side the electromagnetic theory was consolidated on the 19th century, the emergence of the special and the general relativity theories on the 20th century opened possibilities of further…
In this paper we study the nonlocal effects of noncommutative spacetime on simple physical systems. Our main point is the assumption that the noncommutative effects are consequences of a background field which generates a local spin…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical…
These notes comprise the first of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. This first part deals solely with the classical theory on a noncommutative torus.…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…
We propose an alternative interpretation for the meaning of noncommutativity of the string-inspired field theories and quantum mechanics. Arguments are presented to show that the noncommutativity generated in the stringy context should be…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…