Manifest Covariant Hamiltonian Theory of General Relativity

Abstract

The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.

References in corpus (1)

• Synchronous Lagrangian variational principles in General Relativity

Cited by in corpus (4)

• Quantum-wave equation and Heisenberg inequalities of covariant quantum gravity
• Particle creation and reheating in a braneworld inflationary scenario
• Lagrangian formalism in the theory of relativistic vector fields
• Loop quantum gravity with optimal control path integral, and application to black hole tunneling