Related papers: Relational Evolution of Observables for Hamiltonia…

The generalization of the concept of interaction-free evolutions (IFE) [A. Napoli, {\it et al.}, Phys. Rev. A {\bf 89}, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows…

In a parametrized and constrained Hamiltonian system, an observable is an operator which commutes with all (first-class) constraints, including the super-Hamiltonian. The problem of the frozen formalism is to explain how dynamics is…

A number of positive and null results on the time variation of fundamental constants have been reported. It is difficult to judge whether or not these claims are mutually consistent, since the observable quantities depend on several…

The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…

The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…

We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the…

We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…

This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…

We describe a rigorous construction, using matched asymptotic expansions, which establishes under very general conditions that local terrestrial and solar-system experiments will measure the effects of varying `constants' of Nature…

With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…

Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their…

Noether's symmetry transformations for higher-order lagrangians are studied. A characterization of these transformations is presented, which is useful to find gauge transformations for higher-order singular lagrangians. The case of…

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account to gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle…

A relativistic generalization of the rational Calogero model is obtained by using the deformation of a gauging matrix system with extra semi-dynamical variables. The Hamiltonian of this system is derived by imposing the gauge fixing…

Certain dissipative physical systems closely resemble Hamiltonian systems in $\mathbb{R}^{2n}$, but with the canonical equation for one of the variables in each conjugate pair rescaled by a real parameter. To generalise these dynamical…

An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…

This letter describes a novel derivation of general relativity by considering the (non)self-consistency of theories whose Hamiltonians are constraints. The constraints, from Hamilton's equations, generate the evolution, while the evolution,…

The aim of this paper is to introduce and analyze a new gauge symmetry that appears in complex holomorphic systems. This symmetry allow us to project the system, using different gauge conditions, to several real systems which are connect by…