Related papers: Refined algebraic quantisation in a system with no…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
We show that the associative algebra structure can be incorporated in the BRST quantization formalism for gauge theories such that extension from the corresponding Lie algebra to the associative algebra is achieved using operator…
Renormalized gauge-invariant observables in gauge theories form an algebra which is obtained as the cohomology of the derivation $[\textbf{Q}_L, -]$ with $\textbf{Q}_L$ the renormalized interacting quantum BRST charge. For a large class of…
A formalism is presented which allows covariant three-dimensional bound-state equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described…
We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be…
Unsupervised representation learning presents new opportunities for advancing Quantum Architecture Search (QAS) on Noisy Intermediate-Scale Quantum (NISQ) devices. QAS is designed to optimize quantum circuits for Variational Quantum…
Retrieval Augmented Generation (RAG) is a common method for integrating external knowledge into pretrained Large Language Models (LLMs) to enhance accuracy and relevancy in question answering (QA) tasks. However, prompt engineering and…
This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…
In this paper we are concerned with the stabilization of MUSCL-type finite volume schemes in arbitrary space dimensions. We consider a number of limited reconstruction techniques which are defined in terms inequality-constrained linear or…
We implement the Hamiltonian treatment of a nonAbelian noncommutative gauge theory, considering with some detail the algebraic structure of the noncommutative symmetry group. The first class constraints and Hamiltonian are obtained and…
We propose a mathematically rigorous unified framework for hybrid quantum mechanics that systematically combines algebraic deformation and spatial non-locality within a single operator formalism. By constructing a self-adjoint hybrid…
The structure functions of the Lagrangian gauge algebra are given explicitly in terms of the hamiltonian constraints and the first order Hamiltonian structure functions and their derivatives.
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
The recently introduced framework of Graded Quantitative Rewriting is an innovative extension of traditional rewriting systems, in which rules are annotated with degrees drawn from a quantale. This framework provides a robust foundation for…
In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $\delta$. We then solve the Hamiltonian constraint for both a self-adjoint, and a…
In this article, we present a novel formulation of the massless Schwinger model-quantum electrodynamics in $1+1$ dimensions-within the framework of Algebraic Quantum Field Theory (AQFT), emphasizing features that transcend the traditional…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
This is the second paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we begin with the simplest examples: Finite dimensional models with…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
Deep Reinforcement Learning (RL) has considerably advanced over the past decade. At the same time, state-of-the-art RL algorithms require a large computational budget in terms of training time to converge. Recent work has started to…