A view on the problems of Quantum Gravity

TL;DR

This paper discusses alternative approaches to quantum gravity that incorporate gauge degrees of freedom and extended phase space, potentially resolving issues in current quantization methods and aligning with principles of General Relativity and Quantum Theory.

Contribution

It proposes a formulation of quantum gravity in extended phase space that maintains invariance under reparametrizations and offers a new perspective on quantum phenomena in different reference frames.

Findings

Classical Hamiltonian dynamics matches Lagrangian dynamics in extended phase space.

Poisson bracket algebra remains invariant under reparametrizations.

Quantum description allows observers to see various complementary gravitational phenomena.

Abstract

The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is missed. A probable alternative is to consider gravitational dynamics in extended phase space, taking into account the distinctions between General Relativity and other field theories. The formulation in extended phase space leads to some consequences at classical and quantum levels. At the classical level, it ensures that Hamiltonian dynamics is fully equivalent to Lagrangian dynamics, and the algebra of Poisson brackets is invariant under reparametrizations in a wide enough class including reparametrizations of gauge variables, meantime in the canonical Dirac approach the constraints' algebra is not invariant that creates problems with quantization. At the quantum level, the approach come to the description in which the observer can see various but complementary quantum gravitational phenomena in different reference frames that answers the spirit of General Relativity and Quantum Theory. Though until now the approach was applied to General Relativity in its original formulations, its implementation in different trends, including Quantum Loop Gravity or some other representations of gravitational variables, would also be of interest.