Related papers: Gauging Newton's Law
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are…
The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of…
It is well known that the equations of motion obtained from Newtons second law of motion can be obtained from a Lagrangian via the Euler-Lagrangian formulation if and only if the equations of motion satisfy the Helmholtz conditions. In this…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
We derive the Hamiltonian formulation of classical mechanics directly, without reference to Lagrangian mechanics. We start from the definition of states in terms of labels used to identify them, and show how, under a deterministic and…
This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…
Using the commutativity of a general variation with the time differentiation we discuss both global and local (gauge) symmetries of a lagrangian from a unified point of view. The Noether considerations are thereby applicable for both cases.…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
We consider gauge theories from the free evolution point of view, in which initial data satisfying constraints of a theory are given. Because the constraints are compatible with the field equations they remain so. We study a model…
This is a review of the constrained dynamical structure of Poincare gauge theory which concentrates on the basic canonical and gauge properties of the theory, including the identification of constraints, gauge symmetries and conservation…
We develop a theory of gauge and dynamical equivalence for Lagrangian systems on Lie algebroids, also studying its relationship with Noether and non-Noether conserved quantities.
The aim of the present article is to describe the symmetry structure of a general gauge (singular) theory, and, in particular, to relate the structure of gauge transformations with the constraint structure of a theory in the Hamiltonian…
The most general gravity Lagrangian in four dimensions contains three topological densities, namely Nieh-Yan, Pontryagin and Euler, in addition to the Hilbert-Palatini term. We set up a Hamiltonian formulation based on this Lagrangian. The…
Newtonian, Lagrangian, and Hamiltonian dynamical systems are well formalized mathematically. They give rise to geometric structures describing motion of a point in smooth manifolds. Riemannian metric is a different geometric structure…
We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to…
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation…
It is argued that quantum mechanics follows naturally from the assumptions that there are no fundamental causal laws but only probabilities for physical processes that are constrained by symmetries, and reality is relational in the sense…
We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an…