Canonical forms for separability structures with less than five Killing tensors
Canonical forms for -structures in pseudo-riemannian manifolds
The hamiltonian formalism in higher order variational problems
I fondamenti epistemologici della Relatività Generale e la sua «eredità matematica»
Si analizzano alcuni aspetti fondazionali della Relatività Generale dal punto di vista epistemologico, dando una particolare rilevanza al fatto che non ha più senso parlare di tempo durante il quale le dinamiche si svolgono, né di spazio in cui le dinamiche hanno luogo. La Relatività Generale afferma infatti l'identificazione tra spazio-tempo – che è una varietà metrica e dunque un'entità a priori non dinamica – e la materia – che soggiace ad equazioni differenziali ed è dunque un'entità dinamica...
On certain transformations for black-holes energetics
È contenuto nell'Introduzione.
General theory of Lie derivatives for Lorentz tensors
We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.
Symmetries in finite order variational sequences
We refer to Krupka’s variational sequence, i.e. the quotient of the de Rham sequence on a finite order jet space with respect to a ‘variationally trivial’ subsequence. Among the morphisms of the variational sequence there are the Euler-Lagrange operator and the Helmholtz operator. In this note we show that the Lie derivative operator passes to the quotient in the variational sequence. Then we define the variational Lie derivative as an operator on the sheaves of the variational sequence. Explicit...
About boundary terms in higher order theories
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particular...
Do Barbero-Immirzi connections exist in different dimensions and signatures?
We shall show that no reductive splitting of the spin group exists in dimension other than in dimension . In dimension there are reductive splittings in any signature. Euclidean and Lorentzian signatures are reviewed in particular and signature is investigated explicitly in detail. Reductive splittings allow to define a global -connection over spacetime which encodes in an weird way the holonomy of the standard spin connection. The standard Barbero-Immirzi (BI) connection used in LQG is...
Locally variational invariant field equations and global currents: Chern-Simons theories
We introduce the concept of conserved current variationally associated with locally variational invariant field equations. The invariance of the variation of the corresponding local presentation is a sufficient condition for the current beeing variationally equivalent to a global one. The case of a Chern-Simons theory is worked out and a global current is variationally associated with a Chern-Simons local Lagrangian.
On the wave equation in curved spacetime
Cauchy data on a manifold
Generalized Jacobi morphisms in variational sequences
Summary: We provide a geometric interpretation of generalized Jacobi morphisms in the framework of finite order variational sequences. Jacobi morphisms arise classically as an outcome of an invariant decomposition of the second variation of a Lagrangian. Here they are characterized in the context of generalized Lagrangian symmetries in terms of variational Lie derivatives of generalized Euler-Lagrange morphisms. We introduce the variational vertical derivative and stress its link with the classical...
General relativity at the turn of the third millennium.
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