Related papers: Refined algebraic quantisation in a system with no…
Retrieval-Augmented Generation (RAG) is increasingly employed in generative AI-driven scientific workflows to integrate rapidly evolving scientific knowledge bases, yet its reliability is frequently compromised by non-determinism in their…
We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…
Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show that fine-tuning these two…
Model quantization is a widely used technique to compress and accelerate deep neural network (DNN) inference. Emergent DNN hardware accelerators begin to support mixed precision (1-8 bits) to further improve the computation efficiency,…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
The Residual Quantization (RQ) framework is revisited where the quantization distortion is being successively reduced in multi-layers. Inspired by the reverse-water-filling paradigm in rate-distortion theory, an efficient regularization on…
We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
\noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. The result is…
The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every…
For large-scale discrete-time algebraic Riccati equations (DAREs) with high-rank nonlinear and constant terms, the stabilizing solutions are no longer numerically low-rank, resulting in the obstacle in the computation and storage. However,…
We develop a renormalization group (RG)-based perturbation scheme for a class of ordinary differential equations, including first-order systems with semisimple or nilpotent linear parts, as well as scalar higher-order equations. The key…
When applying the techniques of Loop Quantum Gravity (LQG) to symmetry-reduced gravitational systems, one first regularizes the scalar constraint using holonomy corrections, prior to quantization. In inhomogeneous system, where a residual…
In this series of papers, we present a set of methods to revive quantum geometrodynamics which encountered numerous mathematical and conceptual challenges in its original form promoted by Wheeler and De Witt. In this paper, we introduce the…
A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…
The design of quantum control methods has been shown to greatly improve the performance of many evolving quantum technologies. To this end, the usage of adiabatic dynamics to drive quantum systems is seriously limited by the action of…
We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components…