Related papers: New coordinates for a simpler canonical derivation…

The Hawking effect is one of the most extensively studied topics in modern physics. Yet it remains relatively under-explored within the framework of canonical quantization. The key difficulty lies in the fact that the Hawking effect is…

We present a derivation of Hawking radiation based on canonical quantization of a massless scalar field in the background of a Schwarzschild black hole using Lemaitre coordinates and show that in these coordinates the Hamiltonian of the…

It is widely believed that the Hawking effect might hold clues to the possible, yet unknown, trans-Planckian physics. On the other hand, one could ask whether the effect itself might be altered by such trans-Planckian physics. We seek an…

We consider a class of Lagrangian theories where part of the coordinates does not have any time derivatives in the Lagrange function (we call such coordinates degenerate). We advocate that it is reasonable to reconsider the conventional…

The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…

Canonical methods are not sufficient to properly quantize space-like axial gauges. In this paper, we obtain guiding principles which allow the construction of an extended Hamiltonian formalism for pure space-like axial gauge fields. To do…

In this talk I show how to canonically quantize a massless scalar field in the background of a Schwarzschild black hole in Lema\^itre coordinates and then present a simplified derivation of Hawking radiation based upon this procedure. The…

This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the…

Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance…

Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…

We study cosmological perturbation theory with scalar field and pressureless dust in the Hamiltonian formulation, with the dust field chosen as a matter-time gauge. The corresponding canonical action describes the dynamics of the scalar…

We develop the formalism for canonical reduction of $(1+1)$--dimensional gravity coupled with a set of point particles by eliminating constraints and imposing coordinate conditions. The formalism itself is quite analogous to the…

Although the deformation of the Heisenberg algebra by a minimal length has become a central tool in quantum gravity phenomenology, it has never been rigorously obtained and is often derived using heuristic reasoning. In this study, we move…

The idea of this contribution is to suggest a way to get rid of gravity as a dynamical space time approximately in cosmology and thus be able to use Hamiltonian formulation ignoring the gravitational degrees of freedom, treating them just…

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice…

To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space-time. The coordinate representations we consider do not possess a singularity at the horizon unlike the…

In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…

We consider the gravitational collapse of self-gravitating spherical dust cloud in the Hamiltonian formalism. We address both homogeneous and inhomogeneous cases. Our novel derivation of the Hamiltonian of the system is based on the…

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum…