Related papers: Covariant Hamiltonian boundary term: Reference and…
Basic principles of the Hamilton approach developed for the metric General Relativity (Einstein`s GR) are discussed. In particular, we derive the Hamiltonian of the metric GR in the explicit form. This Hamiltonian is a quadratic function of…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
A manifestly covariant expression for the current matrix elements of three quark bound systems is derived in the framework of the Point Form Relativistic Hamiltonian Dynamics. The relativistic impulse approximation is assumed in the model.…
Hamiltonian mechanics of field theory can be formulated in a generally covariant and background independent manner over a finite dimensional extended configuration space. The physical symplectic structure of the theory can then be defined…
Combinatorial quantum gravity is governed by a discrete Einstein-Hilbert action formulated on an ensemble of random graphs. There is strong evidence for a second-order quantum phase transition separating a random phase at strong coupling…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
We compare the path integral for transition functions in unimodular gravity and in general relativity. In unimodular gravity the cosmological constant is a property of states that are specified at the boundaries whereas in general…
Nonlocality is a defining feature of quantum mechanics and has long served as a key indicator of quantum resources since the formulation of Bell's inequalities. Identifying the contribution of nonlocality to extractable work remains a…
We consider General Relativity (GR) on a space-time whose spatial slices are compact manifolds $M$ with non-empty boundary $\partial M$. We argue that this theory has a non-trivial space of `vacua', consisting of spatial metrics obtained by…
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a…
We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
An algebraic framework was introduced in our previous works to address the covariance issue in spherically symmetric effective quantum gravity. This paper extends the framework to the electrovacuum case with a cosmological constant. After…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of…
The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are…