Related papers: Quantum differential equations and helices
This lecture reviews aspects of and prospects for progress towards a theory of quantum gravity from a particle physics perspective, also paying attention to recent findings of the LHC experiments at CERN.
The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. Quantum mechanics constrains relationships between kinematic parameters and the coordinates describing the dynamics. Example quantum…
Invited talk presented at the Workshop on Physics at Current Accelerators and the Supercollider, Argonne, Illinois, and at the 17th Johns Hopkins Workshop on Current Problems in Particle Theory, Budapest, Hungary.
In a recent paper, Engle, Hanusch and Thiemann showed that there is a unique state on the reduced holonomy-flux $\ast$-algebra of homogeneous isotropic loop quantum cosmology, that is invariant under residual diffeomorphims. This result has…
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…
The paper has heuristic character. The conceptual frame, based on the assumption of quantum uncertainty only, has been formerly introduced in two papers [S. Tosto, Il Nuovo Cimento B, vol. 111, n.2, 1996 and S. Tosto, Il Nuovo Cimento D,…
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed…
A review of recent developments in the quantum differential calculus. The quantum group $GL_q(n)$ is treated by considering it as a particular quantum space. Functions on $SL_q(n)$ are defined as a subclass of functions on $GL_q(n)$. The…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the…
This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…
This volume contains the proceedings of the 8th International Workshop on Quantum Physics and Logic (QPL 2011), which was held October 27-29, 2011 at Radboud University Nijmegen. The goal of this workshop series is to bring together…
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We develop both…
This mini-course, conducted at the XI School on Geometric, Algebraic, and Topological Methods in Quantum Field Theory held in Villa de Leyva, Colombia, provides an overview of the interconnection between generalized symmetries and…
These notes summarize a set of lectures on phenomenological quantum gravity which one of us delivered and the other attended with great diligence. They cover an assortment of topics on the border between theoretical quantum gravity and…
These lecture notes grew out of notes for courses around Integrable PDEs and the KdV equation given by the authors during the past five years at the University of Antwerp (Belgium). Comments and suggestions are welcome.
We describe recent attempts at discretizing canonical quantum gravity in four dimensions in terms of a connection formulation. This includes a general introduction, a comparison between the real and complex connection approach, and a…
This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.
Quantum cosmology from the late sixties into the early twenty-first century is reviewed and appraised in the form of a debate, set up by two presentations on mainly the Wheeler-DeWitt quantization and on loop quantum cosmology,…