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Journal ArticleDOI

Field and particle equations for the classical Yang-Mills field and particles with isotopic spin

01 Jan 1970-Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields (Springer Berlin Heidelberg)-Vol. 65, Iss: 4, pp 689-694
TL;DR: A complete system of equations describing the interaction between the Yang-Mills field and isotopic-spin-carrying particles in the classical limit is extracted from the equations of motion for the quantum fields.
Abstract: A complete system of equations describing the interaction between the Yang-Mills field and isotopic-spin-carrying particles in the classical limit is extracted from the equations of motion for the quantum fields. Some simple consequences are derived. The consistency of the equations is investigated.
Citations
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MonographDOI
08 Aug 2006
TL;DR: Geodesics in subriemannian manifolds: Dido meets Heisenberg Chow's theorem: Getting from A to B A remarkable horizontal curve Curvature and nilpotentization Singular curves and geodesics A zoo of distributions Cartan's approach The tangent cone and Carnot groups Discrete groups tending to Carnot geometries Open problems Mechanics and geometry of bundles: Metrics on bundles Classical particles in Yang-Mills fields Quantum phases Falling, swimming, and orbiting Appendices: Geometric mechanics Bundles and the Hopf fibration The S
Abstract: Geodesics in subriemannian manifolds: Dido meets Heisenberg Chow's theorem: Getting from A to B A remarkable horizontal curve Curvature and nilpotentization Singular curves and geodesics A zoo of distributions Cartan's approach The tangent cone and Carnot groups Discrete groups tending to Carnot geometries Open problems Mechanics and geometry of bundles: Metrics on bundles Classical particles in Yang-Mills fields Quantum phases Falling, swimming, and orbiting Appendices: Geometric mechanics Bundles and the Hopf fibration The Sussmann and Ambrose-Singer theorems Calculus of the endpoint map and existence of geodesics Bibliography Index.

1,143 citations

Book
29 May 1992
TL;DR: The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering as mentioned in this paper, and the main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibrium and chaos in mechanical systems.
Abstract: Publisher's description: The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. In this book, Professor Marsden concentrates on these geometric aspects, especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule.

503 citations


Cites background from "Field and particle equations for th..."

  • ...For a start on the numerical analysis of symplectic integrators, see SanzSerna [1988], Simo, Tarnow, and Wong [1992] and related papers....

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Journal ArticleDOI
TL;DR: In this article, the authors provide a practitioners' guide to features of the Dyson-Schwinger equations and canvasses phenomenological applications to light meson and baryon properties in cold, sparse QCD.

468 citations

Journal ArticleDOI
TL;DR: In this paper, a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling g is sufficiently small to allow for weak coupling calculations is presented.

413 citations

Book
01 Jul 2001
TL;DR: The Lagrange Poincare category as discussed by the authors is a Lagrangian analogue of the bundle picture on the Hamiltonian side of the Lagrange-Routh equation, and it can be seen as a Lagrange analog of the category of Poisson manifolds in Hamiltonian theory.
Abstract: This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler{Poincare reduction (for the case in which the conguration space is a Lie group) as well as Euler-Poincare reduction for semidirect products. The context established for this theory is a Lagrangian analogue of the bundle picture on the Hamiltonian side. In this picture, we develop a category that includes, as a special case, the realization of the quotient of a tangent bundle as the Whitney sum of the tangent of the quotient bundle with the associated adjoint bundle. The elements of this new category, called the Lagrange{Poincare category, have enough geometric structure so that the category is stable under the procedure of Lagrangian reduction. Thus, reduction may be repeated, giving the desired context for reduction by stages. Our category may be viewed as a Lagrangian analog of the category of Poisson manifolds in Hamiltonian theory. We also give an intrinsic and geometric way of writing the reduced equations, called the Lagrange{Poincare equations, using covariant derivatives and connections. In addition, the context includes the interpretation of cocycles as curvatures of connections and is general enough to encompass interesting situations involving both semidirect products and central extensions. Examples are given to illustrate the general theory. In classical Routh reduction one usually sets the conserved quantities conjugate to the cyclic variables equal to a constant. In our development, we do not require the imposition of this constraint. For the general theory along these lines, we refer to the complementary work of Marsden, Ratiu and Scheurle [2000], which studies the Lagrange-Routh equations.

266 citations

References
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Journal ArticleDOI
TL;DR: In this article, it was pointed out that the usual principle of invariance under isotopic spin rotation is not consistant with the concept of localized fields, and the possibility of having invariance in local isotope spin rotations was explored.
Abstract: It is pointed out that the usual principle of invariance under isotopic spin rotation is not consistant with the concept of localized fields. The possibility is explored of having invariance under local isotopic spin rotations. This leads to formulating a principle of isotopic gauge invariance and the existence of a b field which has the same relation to the isotopic spin that the electromagnetic field has to the electric charge. The b field satisfies nonlinear differential equations. The quanta of the b field are particles with spin unity, isotopic spin unity, and electric charge $\ifmmode\pm\else\textpm\fi{}e$ or zero.

2,635 citations