Related papers: Vector coherent state representations and their in…
Word meaning has different aspects, while the existing word representation "compresses" these aspects into a single vector, and it needs further analysis to recover the information in different dimensions. Inspired by quantum probability,…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
We introduce the construction of induced corepresentations in the setting of locally compact quantum groups and prove that the resulting induced corepresentations are unitary under some mild integrability condition. We also establish a…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
Recognizing elementary underlying concepts from observations (disentanglement) and generating novel combinations of these concepts (compositional generalization) are fundamental abilities for humans to support rapid knowledge learning and…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose…
The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra $[\hat J,U]=U$, where $U$ is unitary, which is a direct…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to…
The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…
The purpose of this paper is to articulate an observation that many interesting type of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. This extends…
The exact and stable evolutions of generalized coherent states (GCS) for quantum systems are considered by making use of the time-dependent integrals of motion method and of the Klauder approach to the relationship between quantum and…
Although the latent spaces learned by distinct neural networks are not generally directly comparable, recent work in machine learning has shown that it is possible to use the similarities and differences among latent space vectors to derive…
Richard Stanley played a crucial role, through his work and his students, in the development of the relatively new area known as combinatorial representation theory. In the early stages, he has the merit to have pointed out to…
A summary of the construction procedure of generalized versions of Baxter's Q-operator is given. Illustrated by several figures and diagrams the use of representation theory is explained step-by-step avoiding technical details. The relation…
A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral…
Large language models, like transformers, have recently demonstrated immense powers in text and image generation. This success is driven by the ability to capture long-range correlations between elements in a sequence. The same feature…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…