Poincare-Cartan form for scalar fields in curved background

Details Poincare-Cartan form for scalar fields in curved background Poincare-Cartan form for scalar fields in curved background

2011-04-27

arxiv.org/abs/1104.5095v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX2e, 18 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Poincare-Cartan form for scalar fields in curved background does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Poincare-Cartan form for scalar fields in curved background, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Poincare-Cartan form for scalar fields in curved background will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-475361