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 (7)

• Spacetime states and covariant quantum theory
• The Hamiltonian formulation of General Relativity: myths and reality
• Diffeomorphism Invariance in the Hamiltonian formulation of General Relativity
• Spacetime Covariant Form of Ashtekar's Constraints
• Synchronous Lagrangian variational principles in General Relativity
• Hamiltonian formulation for the classical EM radiation-reaction problem: application to the kinetic theory for relativistic collisionless plasmas
• Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles

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• Space-time second-quantization effects and the quantum origin of cosmological constant in covariant quantum gravity
• Tachyon with an inverse power-law potential in a braneworld cosmology
• Particle creation and reheating in a braneworld inflationary scenario
• Griffiths Variational Multisymplectic Formulation for Lovelock Gravity
• Lagrangian formalism in the theory of relativistic vector fields
• Loop quantum gravity with optimal control path integral, and application to black hole tunneling