Related papers: New Trend in Quantization Methods
This is an extended version of the talk given by the Author at the 40th Symposium on Mathematical Physics held in Torun, Poland, June 25-28, 2008. We review the methods of canonical quantization of free particle motion on curved…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
The presentations, discussions and findings from the inaugural `PhyStat-$\nu$' workshop held at the Kavli Institute for the Physics and Mathematics of the Universe (IPMU) near Tokyo in 2016 are described. PhyStat-$\nu$ was the first…
A general semiclassical approach to quantum systems with system-bath interactions is developed. We study system decoherence in detail using a coherent state semiclassical wavepacket method which avoids singularity issues arising in the…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures.…
We propose in this paper an alternative method for the quantisation of systems with first-class constraints. This method is a combination of the coherent-state-path-integral quantisation developed by Klauder, with the ideas of reduced state…
We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
In this letter, we address the problem of developing quantum state tomography (QST) methods that remain valid at any time during a sequence of measurements. Specifically, the aim is to provide a rigorous quantification of the uncertainty…
Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers…
This is an expanded version of the notes by the second author of the lectures on Hitchin systems and their quantization given by the first author at the Beijing Summer Workshop in Mathematics and Mathematical Physics ``Integrable Systems…
The results, different aspects and applications of our method of quantisation on configuration manifolds - called Borel Quantisation - were presented at meetings of the series `Symmetries in Science' and can be found in the published…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
Based on the model's resilience to computational noise, model quantization is important for compressing models and improving computing speed. Existing quantization techniques rely heavily on experience and "fine-tuning" skills. In the…
Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced…
Aimed at introducing readers to the physics of strongly correlated many-body systems, these notes focus on numerical methods, with detailed discussions on implementing working code for exact diagonalization. A brief introduction to tensor…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…