A. M. Arthurs

Helicity and variational principles for Maxwell's equations

The connection is established between helicity and the action associated with recent canonical variational principles for the equations of the electromagnetic field.

A variational principle for Maxwell's equations

Using a canonical approach, we present a direct variational formulation for the equations of the electromagnetic field in terms of the field vectors.

Complementary variational principles for Maxwell's equations II

New complementary variational principles for Maxwells equations are derived from a canonical formulation in which potentials and field vectors constitute the conjugate variables.

Variational principles for Maxwell's equations II

New variational principles for the electromagnetic field arc derived in terms of the field vectors within a canonical framework.

Bounds for the resistance of a conductor of a given form

New upper and lower bounds for the resistance of a. conductor of given form are derived in a unified manner from the canonical theory of complementary extremum principles.

Duality transformation and invariants of the electromagnetic field

The structure of Maxwells equations under duality transformation and its connection with the work of Heaviside (1885) are discussed. A scheme for generating the associated invariants is also presented.

An extension of a conservation law for the electromagnetic field

A conservation law for current-free electromagnetic fields derived by Lipkin is extended to include certain types of current distribution.

Canonical and duality transformations for the electromagnetic field

In earlier papers we have given a new hamiltonian formulation of the source-free electromagnetic field. In this paper we show that the most general linear canonical transformation with constant coefficients which leaves the form of the field equations and the hamiltonian invariant is the duality transformation. Other invariant quantities of physical interest are also discussed.

Angular momentum and helicity of electromagnetic fields

In this paper we connect the spin angular momentum of a source-free electromagnetic field with the helicities of the vector potentials describing the field.

Conserved quantities in electromagnetic theory

A method of constructing conserved quantities associated with an electromagnetic field is given and the particular ones which can arise from field intensities, vector potentials and Hertz potentials are obtained and related to known results.