相关论文: Involution and Constrained Dynamics I: The Dirac A…

The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…

We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…

The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.

We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom…

The Dirac particle, i.e. the dynamic system S_D, described by the free Dirac equation is investigated. Although the Dirac equation is written usually in the relativistically covariant form, the dynamic system S_D is not completely…

Dynamical systems, described by Lagrangians with first- and second-class constraints, are investigated. In the Dirac approach to the generalized Hamiltonian formalism, the classification and separation of the first- and second-class…

In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…

Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…

In this paper, we study some new properties of Sadik transform such as integration, time delay, initial value theorem, and final value theorem. Moreover, we prove the theorem of Sadik transform for Caputo fractional derivative and we also…

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not…

We propose a method to simulate a Dirac or Majorana equation evolving under a potential with the use of the corresponding free evolution, while the potential dynamics is encoded in a static transformation upon the initial state. We extend…

Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…

We will pick up the concepts of partial and complete observables introduced by Rovelli in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different…

This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between…

This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus…

From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).…

Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant.…

Conventional deep learning prioritizes unconstrained optimization, yet biological systems operate under strict metabolic constraints. We propose that these physical constraints shape dynamics to function not as limitations, but as a…