Related papers: What kind of noncommutative geometry for quantum g…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
We review the construction of particle physics models in the framework of non-commutative geometry. We first give simple examples, and then progress to outline the Connes-Lott construction of the standard Weinberg-Salam model and our…
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…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
This is an introduction for nonspecialists to the noncommutative geometric approach to Planck scale physics coming out of quantum groups. The canonical role of the `Planck scale quantum group' $C[x]\bicross C[p]$ and its observable-state…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong…
Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
We discuss the renormalization properties of noncommutative supersymmetric theories. We also discuss how the gauge field plays a role similar to gravity in noncommutative theories.
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups,…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.