Related papers: Obstacles to the quantization of general relativit…

The formulation of a relativistic dynamical problem as a system of Hamilton equations by respecting the principles of Relativity is a delicate task, because in their classical form the Hamilton equations require the use of a time…

Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral…

We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…

It is often argued that gravity has to be a quantum theory simply because a fundamentally semiclassical approach would necessarily be inconsistent. Here I review recent Newtonian toy models of (stochastic) semiclassical gravity. They…

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…

Simplicial formal maps were introduced in the first paper, (math.QA/0512032), of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a…

The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the…

We study a general relativistic particle action obtained by incorporating the Hamiltonian constraints into the formalism as a toy model for general relativity and string theory. We show how a non-vanishing cosmological constant and a…

The polysymplectic phase space of covariant Hamiltonian field theory can be provided with the current algebra bracket.

We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…

I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…

A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…

The multisymplectic Hamiltonian formalism is a generalization of the Hamiltonian formalism that manifestly preserves covariance in the description of fields and that has been proposed as a possible framework for developing a…

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…

The purpose of this note is to point out that a naive application of symplectic integration schemes for Hamiltonian systems with constraints such as SHAKE or RATTLE which preserve holonomic constraints encounters difficulties when applied…

This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods…

We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such…

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…

We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…

Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf…