Related papers: Integrable structures and the quantization of free…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
The principles of quantum field theory in flat spacetime suggest that gravity is mediated by a massless particle with helicity $\pm2$, the so-called graviton. It is regarded as textbook knowledge that, when the self-coupling of a particle…
The null surfaces of a spacetime act as one-way membranes and can block information for a corresponding family of observers (time-like curves). Since lack of information can be related to entropy, this suggests the possibility of assigning…
We construct Poisson vertex algebra (PVA) structures on arc spaces from $1$-shifted symplectic (QP) data. A Hamiltonian satisfying the classical master equation induces a canonical PVA $\lambda$-bracket, matching the Hamiltonian-operator…
The history of general relativity suggests that in absence of experimental data, constructing a theory on philosophical first principles can lead to a very useful theory as well as to ground-breaking insights about physical reality. The two…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in "natural form",…
We submit a classical unification of the special and general relativities via the new isominkowskian geometry in which the two relativities are differentiated by the basic unit. We then show that the unification admits an operator image in…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
The fully coupled dynamic interaction problem of the free surface of an incompressible fluid and a rigid body beneath it, in an inviscid, irrotational framework and in the absence of surface tension, is considered. Evolution equations of…
The Geroch group is an infinite dimensional transitive group of symmetries of classical cylindrically symmetric gravitational waves which acts by non-canonical transformations on the phase space of these waves. Here this symmetry is…
We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be…
The gravitational interaction, as described by the Einstein-Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure…
The unification of quantum theory and the general theory of relativity - describing gravity, is one of the most important challenges in science. Einstein's general theory of relativity is based on the principle of equivalence, and has been…