Related papers: Lectures on Constrained Systems
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
These notes were delivered as a series of NIMROD lectures at the Rutherford Appleton Laboratory by the author in February 1976 (RL-76-022). The purpose of these lectures was primarily two-fold: to discuss the classical theory of free point…
It is well known that the imposition of a constraint can transform the properties of critical systems. Early work on this phenomenon by Essam and Garelick, Fisher, and others, focused on the effects of constraints on the leading critical…
We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…
These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the…
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard…
Three small lectures are devoted to three Newton's laws, lying in the foundation of classical mechanics. These laws are analyzed from the viewpoint of our contemporary knowledge about space, time and physical interactions. The lectures were…
Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…
Lecture 1 provides an introduction to dynamical electroweak symmetry breaking. Lectures 2 and 3 give an introduction to compositeness, with emphasis on effective lagrangians, power-counting, and the 't Hooft anomaly-matching conditions.
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…