Related papers: Locality, Causality and Noncommutative Geometry

In this work, we generalize the non-geometrical construction of gauge theories, due to S. Deser, to a noncommutative setting. We show that in a free theory, along with the usual local N\"{o}ther current, there is another conserved current,…

Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…

Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type…

A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality…

We present a brief historical introduction to the motivations behind quantum mechanics and quantum field theory on noncommutative spacetime and provide an insightful technique, readily accessible to the undergraduate student, to examine the…

We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the…

In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…

Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…

In this survey article we discuss a framework of noncommutative geometry with differential graded categories as models for spaces. We outline a construction of the category of noncommutative spaces and also include a discussion on…

A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved…

In this thesis we are interested in the problem of dark energy in cosmology. In particular, we consider the possibility that this effect is due to an infrared non-local modification of the theory of General Relativity. Inspired by massive…

We investigate the transformation from ordinary gauge field to noncommutative one which was introduced by N.Seiberg and E.Witten (hep-th/9908142). It is shown that the general transformation which is determined only by gauge equivalence has…

The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This…

We provide a systematic and updated discussion of a research line carried out by our group over the last few years, in which gravity is modified at cosmological distances by the introduction of nonlocal terms, assumed to emerge at an…

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its…

It is a very well known fact that the energy conditions concerning Lorentzian wormhole (WH) solutions of Einstein equations are violated. Consequently, attempts to avoid the violation of the energy conditions constitutes one of the main…

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…

Theory of electromagnetic field, specified by an effective action functional, is considered. The causality condition is imposed in the form of a requirement that the group velocities of propagation of small and soft disturbances over the…

In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…

A calculation by Jacobson [1] strongly implies that the field equations which describe gravity are emergent phenomena. In this paper, the method is extended to the case of a non-commutative spacetime. By making use of a non-commutative…