Exact Solutions of Classical Electrodynamics and the Yang--Mills--Wong Theory in Even-Dimensional Spacetime

Exact solutions of classical gauge theories in even-dimensional (D=2n) spacetimes are discussed. Common and specific properties of these solutions are analyzed for the particular dimensions D=2, D=4, and D=6. A consistent formulation of classical gauge field theories with pointlike charged or colored particles is proposed for D=6. The particle Lagrangian must then depend on the acceleration. The self-interaction of a point particle is considered for D=2 and D=6. In D=2, radiation is absent and all processes are reversible. In D=6, the expression for the radiation rate and the equation of motion of a self-interacting particle are derived; from which follows that the Zitterbewegung always leads to radiation. It is shown that non-Abelian solutions are absent for any D not equal to 4; only Coulomb-like solutions, which correspond to the Abelian limit of the D-dimensional Yang--Mills--Wong theory, are admitted.Comment: LaTeX 2.09, 16 page

Self-accelerated Universe

It is widely believed that the large redshifts for distant supernovae are explained by the vacuum energy dominance, or, in other words, by the cosmological constant in Einstein's equations, which is responsible for the anti-gravitation effect. A tacit assumption is that particles move along a geodesic for the background metric. This is in the same spirit as the consensus regarding the uniform Galilean motion of a free electron. However, there is a runaway solution to the Lorentz--Dirac equation governing the behavior of a radiating electron, in addition to the Galilean solution. Likewise, a runaway solution to the entire system of equations, both gravitation and matter equations of motion including, may provide an alternative explanation for the accelerated expansion of the Universe, without recourse to the hypothetic cosmological constant.Comment: 11 pages; Talk at the 9th Adriatic Meeting, Dubrovnic, Croatia, 4-14 September, 2003, Minor improvement, references added; to appear in ``Progress in General Relativity and Quantum Cosmology Research'', Nova Science Publisher

Holography and two phases of the QCD vacuum

The holographic principle is often (and hastily) attributed to quantum gravity and domains of the Planck size. Meanwhile it can be usefully applied to problems where gravitation effects are negligible and domains of less exotic size. The essence of this principle is that any physical system can be taken to be either classical, placed in a D+1-dimensional spacetime, or quantum-mechanical, located in its D-dimensional boundary. For example, one believes that a hydrogen atom is a typical quantum system living in a four-dimensional spacetime, but it can also be conceived as a classical system living in a five-dimensional embracing spacetime. The subnuclear realm is more intricate since the gluon vacuum reveals two phases, the hadronic and plasma phases. They differ in energetics and symmetry. Moreover, the classical four-dimensional picture is pertinent to the behavior of constituent quarks while the plasma phase is expected to be grasped by standard four-dimensional QCD. The relation between the holographic standpoint and the symmetry treatment of these two phases is outlined. Exact retarded solutions to the classical SU(N) four-dimensional Yang-Mills equations with the source composed of several point-like colored particles is considered. Features of these solutions in the large-N limit provide insight into the gauge symmetries of two gluon vacua.Comment: LaTeX 2.09, 8 pages, 2 figure; talk at the 6th Workshop on non-perturbative QCD, 5-9 June 2001, American University of Pari

Massless interacting particles

We show that classical electrodynamics of massless charged particles and the Yang--Mills theory of massless quarks do not experience rearranging their initial degrees of freedom into dressed particles and radiation. Massless particles do not radiate. We consider a version of the direct interparticle action theory for these systems following the general strategy of Wheeler and Feynman.Comment: LaTeX; 20 pages; V4: discussion is slightly modified to clarify some important points, relevant references are adde

Is classical reality completely deterministic?

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all autonomous classical systems. We give counterexamples of this view. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension shows that the solution to the Cauchy problem with the initial conditions of a particular type is not unique. Therefore, random behavior of closed classical systems is indeed possible. This finding provides a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.Comment: Replace the paper with a revised versio