  Poincare-Cartan form for scalar field is constructed as a differential 4-form
in a `directly Hamiltonian' formalism which does not use a Lagrangian. The
canonical momentum $p$ of a scalar field $\phi$ is a 1-form and the
Poincare-Cartan 4-form $\Theta$ is $(*p)\ww d\phi-H$ where the Hamiltonian $H$
is a suitable 4-form made from $\phi$ and $p$ using the Hodge star operator
defined by the Riemannian metric of the background spacetime. An allowed field
configuration is a 4-dimensional surface in the 9-dimensional extended phase
space such that its tangent vectors annihilate $\Omega=-d\Theta$. Relation of
this to variational principle, symmetry fields and conserved quantities is
worked out. Observables are defined as differential 4-forms constructed from
field and momenta smeared with appropriate test functions. A bracket defined by
Peierls long ago is found to be the suitable candidate for quantization.
