Related papers: Visualizing 2D Quantum Field Theory: Geometry and …
We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable, but not conformal invariant. Questions concerning the $\b$ function and the effective action are addressed, and the effective action and the…
Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Such choices can be reformulated in terms of a topological…
Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
Though the mediums for visualization are limited, the potential dimensions of a dataset are not. In many areas of scientific study, understanding the correlations between those dimensions and their uncertainties is pivotal to mining useful…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…
In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.
In this note we provide a gentle introduction to the concepts and intuition behind the recent breakthrough results on the mathematically rigorous construction of a non-trivial 2D conformal field theory, namely the so-called Liouville…
Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…
Visualizations have played a crucial role in helping quantum computing users explore quantum states in various quantum computing applications. Among them, Bloch Sphere is the widely-used visualization for showing quantum states, which…
We study characteristics of quantum evolution which can be called curvature and torsion. The curvature shows a deviation of the state vector in quantum evolution from the geodesic line. The torsion shows a deviation of state vector from the…
It is shown that the attempt to extend the notion of ideal measurement to quantum field theory leads to a conflict with locality, because (for most observables) the state vector reduction associated with an ideal measurement acts to…
This paper explores the distinction between virtual and real photons in the context of the Davies quantum relativistic extension of the Wheeler-Feynman classical electromagnetic theory. An alternative way of understanding this distinction…
Non-isotropic geometries are of interest to low-dimensional topologists, physicists and cosmologists. However, they are challenging to comprehend and visualize. We present novel methods of computing real-time native geodesic rendering of…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence…
Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…