  In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the
potentials $A^{\mu}$ are taken as the dynamical variables. In this paper I take
the electric field $\vec{E}$ and the magnetic field $\vec{B}$ as the the
dynamical variables. I find a Lagrangian that gives the dynamical Maxwell
equations and include the constraint equations by using Lagrange multipliers.
In passing to the Hamiltonian one finds that the canonical momenta
$\vec{\Pi}_E$ and $\vec{\Pi}_B$ are constrained giving 6 second class
constraints at each point in space. Gauss's law and
$\vec{\nabla}\cdot\vec{B}=0$ can than be added in as additional constraints.
There are now 8 second class constraints, leaving 4 phase space degrees of
freedom. The Dirac bracket is then introduced and is calculated for the field
variables and their conjugate momenta.
