Related papers: Geometry of Quantum Projective Spaces
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
We explore the relation between noncommutative geometry, in the spectral triple formulation, and quantum mechanics. To this aim, we consider a dynamical theory of a noncommutative geometry defined by a spectral triple, and study its…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.
MSc thesis of the author offering an introduction to the operator algebraic approach to noncommutative geometry, with a treatment of some more advanced elements such as the noncommutative geometry of quantum groups, fuzzy physics, and…
We briefly describe how to introduce the basic notions of noncommutative differential geometry on the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$.
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
Quantum states naturally represent symmetry groups, though often in a projective sense. Intriguingly, the projective nature of crystalline symmetries has remained underexplored until very recently. A series of groundbreaking theoretical and…
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices $M_2(\C)=\C\Z_2\cdot\C\Z_2$. We also further extend the coalgebra…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
A new space namely the Weyl-Kahler is proposed to the quantum state space. Some of the physical consequences are discussed.
This paper is an adaptation of a chapter from an upcoming monograph on noncommutative geometry and quantum groups. We present examples of non compact quantum groups which are deformations of low dimensional Lie groups. The paper is of…