Related papers: Quantum Features of Non-Symmetric Geometries
We study some discrete symmetries of unbiased (Hadamard) and biased quantum walk on a line, which are shown to hold even when the quantum walker is subjected to environmental effects. The noise models considered in order to account for…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
The geometric phase can be used as a fruitful venue of investigation to infer features of the quantum systems. Its application can reach new theoretical frontiers and imply innovative and challenging experimental proposals. Herein, we take…
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…
A purely geometrical relativity theory results from a construction that produces from three-dimensional space a happy unification of Kaluza's five-dimensional theory and Weyl's conformal theory. The theory can provide geometrical…
Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
A universe much like the (Euclidean) de Sitter space-time appears as background geometry in the causal dynamical triangulation (CDT) regularization of quantum gravity. We study the geometry of such universes which appear in the path…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the conventional geometric gate operation,…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
The state of a quantum system acquires a phase factor, called the geometric phase, when taken around a closed trajectory in the parameter space, which depends only on the geometry of the parameter space. Due to its sensitive nature, the…
In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc elements such as unphysical matter. The same…
For decades, mathematical physicists have searched for a coordinate independent quantization procedure to replace the ad hoc process of canonical quantization. This effort has largely coalesced into two distinct research programs: geometric…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
Studies in string theory and in quantum gravity suggest the existence of a finite lower bound to the possible resolution of lengths which, quantum theoretically, takes the form of a minimal uncertainty in positions $\Delta x_0$. A finite…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups,…