Related papers: Non-Commutative Worlds and Classical Constraints
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…
The gauge connections corresponding to electromagnetism, Yang-Mills theory and Einstein gravity can be derived by assuming specific commutation relations between the phase-space variables of a first quantized theory. Extending the procedure…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
Motivated by the quantum description of gauge theories, we study the cosmological effects of relaxing the Hamiltonian and momentum constraints in general relativity and Gauss' law in electromagnetism. We show that the unconstrained theories…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
The purpose of this paper is to seek a connection between noncommutative geometry, an offshoot of string theory, and certain aspects of dark matter and dark energy. The former case is based on a simple mathematical argument showing that the…
We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…
In some recent theories including Quantum SuperString theory we encounter duality - it arises due to a non commutative geometry which in effect adds an extra term to the Heiserberg Uncertainity Principle. The result is that the micro world…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
Recently, some problems have been found in the definition of the partial derivative in the case of the presence of both explicit and implicit functional dependencies in the classical analysis. In this talk we investigate the influence of…
We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…