Born renormalization in classical Maxwell electrodynamics

We define and compute the renormalized four-momentum of the composed physical system: classical Maxwell field interacting with charged point particles. As a `reference' configuration for the field surrounding the particle, we take the Born solution. Unlike in the previous approach [Gen. Relat. Grav. 26 (1994) 167; Acta Phys. Pol. A 85 (1994) 771; Commun. Math. Phys. 198 (1998), 711], based on the Coulomb `reference', a dependence of the four-momentum of the particle (`dressed' with the Born solution) upon its acceleration arises in a natural way. This will change the resulting equations of motion. Similarly, we treat the angular momentum tensor of the system.Comment: LaTeX file, 20 page

A Gauge-invariant Hamiltonian Description of the Motion of Charged Test Particles

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is used to derive the corresponding Hamiltonian formulation. For this purpose a Hamiltonian description of the theories derived from the second-order Lagrangian is presented. Unlike in the standard approach, the canonical momenta arising here are explicitely gauge-invariant and have a clear physical intepretation. The reduced symplectic form is equaivalent to the Souriau's form. This approach illustrates a new method of deriving equations of motion from field equations.Comment: LATEX, 15 page

A geometric analysis of the Maxwell field in a vicinity of a multipole particle and new special functions

A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies considerably the equations. The solution is given in terms of a series, where a new family of special functions arises in a natural way. Singular behaviour of the field near to the particle may be analyzed this way up to an arbitrary order. Application to the self-interaction problems in classical electrodynamics is discussed.Comment: 33 pages, LaTeX fil

Hamiltonian Structure for Classical Electrodynamics of a Point Particle

We prove that, contrary to the common belief, the classical Maxwell electrodynamics of a point-like particle may be formulated as an infinite-dimensional Hamiltonian system. We derive well defined quasi-Hamiltonian which possesses direct physical interpretation being equal to the total energy of the composed (field + particle) system. The phase space of this system is endowed with an interesting symplectic structure. We prove that this structure is strongly non-degenerated and, therefore, enables one to define consistent Poisson bracket for particle's and field degrees of freedom. We stress that this formulation is perfectly gauge-invariant.Comment: 36 pages, LATE

A Poisson Bracket on Multisymplectic Phase Space

A new Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined. At least for forms of degree n-1, where n is the dimension of space-time, Jacobi's identity is fulfilled.Comment: Invited Talk on XXXII Symposium on Mathematical Physics, Torun (Poland) June 2000 Updated, see note added at the en

Universality of affine formulation in General Relativity theory

Affine variational principle for General Relativity, proposed in 1978 by one of us (J.K.), is a good remedy for the non-universal properties of the standard, metric formulation, arising when the matter Lagrangian depends upon the metric derivatives. Affine version of the theory cures the standard drawback of the metric version, where the leading (second order) term of the field equations depends upon matter fields and its causal structure violates the light cone structure of the metric. Choosing the affine connection (and not the metric one) as the gravitational configuration, simplifies considerably the canonical structure of the theory and is more suitable for purposes of its quantization along the lines of Ashtekar and Lewandowski (see http://www.arxiv.org/gr-qc/0404018). We show how the affine formulation provides a simple method to handle boundary integrals in general relativity theory.Comment: 38 pages, no figures, LaTeX+BibTex, corrected (restructured contents, one example removed, no additional results, typos fixed) versio

Dynamics of a self-gravitating shell of matter

Dynamics of a self-gravitating shell of matter is derived from the Hilbert variational principle and then described as an (infinite dimensional, constrained) Hamiltonian system. A method used here enables us to define singular Riemann tensor of a non-continuous connection {\em via} standard formulae of differential geometry, with derivatives understood in the sense of distributions. Bianchi identities for the singular curvature are proved. They match the conservation laws for the singular energy-momentum tensor of matter. Rosenfed-Belinfante and Noether theorems are proved to be still valid in case of these singular objects. Assumption about continuity of the four-dimensional spacetime metric is widely discussed.Comment: publishe