JMP: Classical Mechanics and Classical Fields

Classical group field theory

Joseph Ben Geloun
The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and then, on more involved nonlocal theories (colored and noncolored) defined over a tensor product of the same group, we address the is ... [J. Math. Phys. 53, 022901 (2012)] published Thu Feb 9, 2012.

Limitations on cloning in classical mechanics

Aaron Fenyes
In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, ... [J. Math. Phys. 53, 012902 (2012)] published Thu Jan 12, 2012.

Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems

Ian Marquette
We recall results concerning one-dimensional classical and quantum systems with ladder operators. We obtain the most general one-dimensional classical systems, respectively, with a third and a fourth-order ladder operators satisfying polynomial Heisenberg algebras. These systems are written in terms ... [J. Math. Phys. 53, 012901 (2012)] published Fri Jan 6, 2012.

Goryachev-Chaplygin, Kovalevskaya, and BrdiCka-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stackel-Killing tensors

G. W. Gibbons and C. Rugina
Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the BrdiCka-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stackel-Killing tensors and that in the case of the pp-wave spacetimes, the symmetry group of th ... [J. Math. Phys. 52, 122901 (2011)] published Fri Dec 23, 2011.

The canonical structure of Podolsky's generalized electrodynamics on the null-plane

M. C. Bertin, B. M. Pimentel, and G. E. R. Zambrano
In this work, we analyze the canonical structure of Podolsky's generalized electrodynamics on the null-plane. We show that the constraint structure presents a set of second-class constraints, which are exclusive of the analysis on the null-plane, and an expected set of first-class ones. An inspectio ... [J. Math. Phys. 52, 102902 (2011)] published Mon Oct 24, 2011.

Non-existence of non-topological solitons in some types of gauge field theories in Minkowski space

Mikhail N. Smolyakov
In this paper the conditions, under which non-topological solitons are absent in the Yang-Mills theory coupled to a nonlinear scalar field in Minkowski space, are obtained in a very simple way. It is also shown that non-topological solitons are absent in the theory describing the massive complex vec ... [J. Math. Phys. 52, 102901 (2011)] published Thu Oct 20, 2011.

Fractal structure of ferromagnets: The singularity structure analysis

Victor K. Kuetche, Thomas B. Bouetou, and Timoleon C. Kofane
Following the Weiss-Tabor-Carnevale approach [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983); J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984).] designed for studying the integrability properties of nonlinear partial differential equations, we investigate the s ... [J. Math. Phys. 52, 092903 (2011)] published Thu Sep 29, 2011.

The origin of the Schott term in the electromagnetic self force of a classical point charge

Michael R. Ferris and Jonathan Gratus
The Schott term is the third order term in the electromagnetic self force of a charged point particle. The self force may be obtained by integrating the electromagnetic stress-energy-momentum tensor over the side of a narrow hypertube enclosing a section of worldline. This calculation has been repea ... [J. Math. Phys. 52, 092902 (2011)] published Mon Sep 26, 2011.

Super central configurations of the three-body problem under the inverse integer power law

Zhifu Xie, Kenyaita Hodge, Krystolyn Henderson, and Michael Westbrook
In this paper, we consider the problem of central configurations of the n-body problem with the general homogenous potential 1/r, where alpha is a positive integer. A configuration q = (q, q, , q) is called a super central configuration if there exists a positive mass vector m = (m, , m) such that q ... [J. Math. Phys. 52, 092901 (2011)] published Wed Sep 14, 2011.

On the Green-functions of the classical off-shell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg

I. Aharonovich and L. P. Horwitz
In previous papers derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter tau). In this paper, we reconcile these derivations resulting in different expl ... [J. Math. Phys. 52, 082901 (2011)] published Thu Aug 11, 2011.

Nonrelativistic Chern-Simons vortices on the torus

N. Akerblom, G. Cornelissen, G. Stavenga, and J. W. van Holten
A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions, which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also c ... [J. Math. Phys. 52, 072901 (2011)] published Thu Jul 28, 2011.

Thomas-forbidden particle capture

John H. Carter and Michael Lieber
At high energies, in particle-capture processes between ions and atoms, classical kinematic requirements show that generally double-collision Thomas processes dominate. However, for certain mass-ratios these processes are kinematically forbidden. This paper explores the possibility of capture for su ... [J. Math. Phys. 52, 062901 (2011)] published Mon Jun 20, 2011.

On the hyperbolicity of Maxwell's equations with a local constitutive law

Volker Perlick
Maxwell's equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell's equations into evolution equations and constraints, we derive the characteristic equation and we discuss its properties in detail. We present several results that ... [J. Math. Phys. 52, 042903 (2011)] published Mon Apr 25, 2011.

Invariant relationships deriving from classical scaling transformations

Sidney Bludman and Dallas C. Kennedy
Because scaling symmetries of the EulerLagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to evolutionary laws that prove useful, even if the transformations are ... [J. Math. Phys. 52, 042902 (2011)] published Tue Apr 19, 2011.

Polynomial constants of motion for Calogero-type systems in three dimensions

Claudia Chanu, Luca Degiovanni, and Giovanni Rastelli
We give an explicit and concise formula for higher degree polynomial first integrals of a family of Calogero-type Hamiltonian systems in dimension three. These first integrals, together with the already known ones, prove the maximal superintegrability of the systems. ... [J. Math. Phys. 52, 032903 (2011)] published Tue Mar 8, 2011.

Wake potentials and impedances of charged beams in gradually tapering structures

D. A. Burton, D. C. Christie, J. D. A. Smith, and R. W. Tucker
We develop an analytical method for calculating the geometric wakefield and impedances of an ultrarelativistic beam propagating on- and off-axis through an axially symmetric geometry with slowly varying circular cross-section, such as a transition. Unlike previous analytical methods, our approach pe ... [J. Math. Phys. 52, 032902 (2011)] published Fri Mar 4, 2011.

Periodic orbits and nonintegrability of generalized classical YangMills Hamiltonian systems

Lidia JimenezLara and Jaume Llibre
The averaging theory of first order is applied to study a generalized YangMills system with two parameters. Two main results are proved. First, we provide sufficient conditions on the two parameters of the generalized system to guarantee the existence of continuous families of isolated periodic orbi ... [J. Math. Phys. 52, 032901 (2011)] published Wed Mar 2, 2011.

Center-of-mass and internal symmetries in classical relativistic systems

Uri Ben-Ya'acov
The internal symmetry of composite relativistic systems is discussed. It is demonstrated that the LorentzPoincare symmetry implies the existence of internal moments associated with the Lorentz boost, which are LaplaceRungeLenz (LRL) vectors. The LRL symmetry is thus found to be the internal symmetry ... [J. Math. Phys. 52, 022903 (2011)] published Tue Feb 22, 2011.

Convergent perturbative power series solution of the stationary MaxwellBornInfeld field equations with regular sources

M. K.-H. Kiessling
The stationary MaxwellBornInfeld field equations of electromagnetism with regular sources rho[is-an-element-of](C[intersection]L)([openface R]) and j[is-an-element-of](C[intersection]L)([openface R]) (componentwise) are solved using a perturbation series expansion in powers of Born's electromagnetic ... [J. Math. Phys. 52, 022902 (2011)] published Tue Feb 8, 2011.

On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory

Juan Carlos Marrero, Narciso Roman-Roy, Modesto Salgado, and Silvia Vilarino
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of Noe ... [J. Math. Phys. 52, 022901 (2011)] published Fri Feb 4, 2011.

Existence of solutions for Hamiltonian field theories by the HamiltonJacobi technique

Danilo Bruno
The paper is devoted to prove the existence of a local solution of the HamiltonJacobi equation in field theory, whence the general solution of the field equations can be obtained. The solution is adapted to the choice of the submanifold where the initial data of the field equations are assigned. Fin ... [J. Math. Phys. 52, 012902 (2011)] published Tue Jan 11, 2011.