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L. Vitagliano

Publications and source records attributed to L. Vitagliano.

18 recordsLinked to original sources
arXiv2013

Partial Differential Hamiltonian Systems

We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in standard multisymplectic approach to Hamiltonian field theory, in our formalism, the geometric structure (kinematics) and the dynamical information on the "phase space" appear as just different components of one single geometric object.

math.DG↗
arXiv2011

Hamilton-Jacobi Diffieties

Diffieties formalize geometrically the concept of differential equations. We introduce and study Hamilton-Jacobi diffieties. They are finite dimensional subdiffieties of a given diffiety and appear to play a special role in the field theoretic version of the geometric Hamilton-Jacobi theory.

math.DG↗
arXiv2010

Secondary Calculus and the Covariant Phase Space

The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w (as first noticed by Zuckerman in 1986) whose degeneracy (functional) distribution is naturally interpreted as the Lie algebra of gauge transformations. We propose a fully rigorous approach to the covariant phase space in the framework of secondary calculus. In particular we describe the degeneracy distribution of w. As a byproduct we rederive the existence of a Lie bracket among gauge invariant functions on the covariant phase space.

math.DG↗
arXiv2010

The Hamilton-Jacobi Formalism for Higher Order Field Theories

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.

math.DG↗
arXiv2010

The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

math.DG↗
arXiv2007

Iterated Differential Forms VI: Differential Equations

We describe the first term of the $Λ_{k-1}\mathcal{C}$--spectral sequence (see math.DG/0610917) of the diffiety (E,C), E being the infinite prolongation of an l-normal system of partial differential equations, and C the Cartan distribution on it.

math.DG↗
arXiv2007

Iterated Differential Forms V: C-Spectral Sequence on Infinite Jet Spaces

In the preceding note math.DG/0610917 the $Λ_{k-1}\mathcal{C}$--spectral sequence, whose first term is composed of \emph{secondary iterated differential forms}, was constructed for a generic diffiety. In this note the zero and first terms of this spectral sequence are explicitly computed for infinite jet spaces. In particular, this gives an explicit description of secondary covariant tensors on these spaces and some basic operations with them. On the basis of these results a description of the $Λ_{k-1}\mathcal{C}$--spectral sequence for infinitely prolonged PDE's will be given in the subsequent note.

math.DG↗
arXiv2006

Iterated Differential Forms III: Integral Calculus

Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms are computed. Various applications and the integral calculus over the algebra $Λ_{\infty}$ will be discussed in subsequent notes.

math.DG↗
arXiv2006

Iterated Differential Forms IV: C-Spectral Sequence

For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the algebra of secondary iterated differential forms on (O,C). This allows to develop secondary tensor analysis on generic diffieties, some simplest elements of which are sketched here. The presented here general theory will be specified to infinite jet spaces and infinitely prolonged PDEs in subsequent notes.

math.DG↗
arXiv2006

Iterated Differential Forms I: Tensors

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed context and, in particular, enriches it with new natural operations. Applications will be considered in subsequent notes.

math.DG↗
arXiv2004

Observational signatures of an electromagnetic overcritical gravitational collapse

We present theoretical predictions for the spectral, temporal and intensity signatures of the electromagnetic radiation emitted during the process of the gravitational collapse of a stellar core to a black hole, during which electromagnetic field strengths rise over the critical value for $e^+e^-$ pair creation. The last phases of this gravitational collapse are studied, leading to the formation of a black hole with a subcritical electromagnetic field, likely with zero charge, and an outgoing pulse of initially optically thick $e^+e^-$-photon plasma. Such a pulse reaches transparency at Lorentz gamma factors of $10^2$--$10^4$. We find a clear signature in the outgoing electromagnetic signal, drifting from a soft to a hard spectrum, on very precise time-scales and with a very specific intensity modulation. The relevance of these theoretical results for the understanding of short gamma-ray bursts is outlined.

astro-ph↗
arXiv2003

On a Separatrix in the Gravitational Collapse to an Overcritical Electromagnetic Black Hole

The dynamical properties of an electron--positron--photon plasma created by the vacuum polarization process occurring around a charged gravitationally collapsing core of an initially neutral star are examined within the framework of General Relativity and Quantum Field Theory. The Reissner--Nordström geometry is assumed to apply between the collapsing core and the oppositely charged remnant of the star. The appearance of a separatrix at radius $\bar{R}$, well outside the asymptotic approach to the horizon, is evidenced. The neutral electron--positron--photon plasma created at radii $r>\bar{R}$ self-propels outwards to infinity, following the classical PEM--pulse analysis. The plasma created at $r<\bar{R}$ remains trapped and follows the gravitational collapse of the core only contributing to the reduction of the electromagnetic energy of the black hole and to the increase of its irreducible mass. This phenomenon has consequences for the observational properties of gamma--ray bursts and is especially relevant for the theoretical prediction of the temporal and spectral structure of the short bursts.

astro-ph↗
arXiv2003

electron-positron-photon plasma around a collapsing star

We describe electron-positron pairs creation around an electrically charged star core collapsing to an electromagnetic black hole (EMBH), as well as pairs annihilation into photons. We use the kinetic Vlasov equation formalism for the pairs and photons and show that a regime of plasma oscillations is established around the core. As a byproduct of our analysis we can provide an estimate for the thermalization time scale.

astro-ph↗
arXiv2003

Plasma expansion in the geometry of a collapsing star

We describe the evolution of an electron-positron-photon plasma created by Sauter--Heisenberg--Euler--Schwinger mechanism around a collapsing charged star core in the Reissner-Nordström geometry external to the core, in view of the application in the framework of the EMBH theory for gamma ray bursts.

astro-ph↗
arXiv2003

On Plasma Oscillations in Strong Electric Fields

We describe the creation and evolution of electron-positron pairs in a strong electric field as well as the pairs annihilation into photons. The formalism is based on generalized Vlasov equations, which are numerically integrated. We recover previous results about the oscillations of the charges, discuss the electric field screening and the relaxation of the system to a thermal equilibrium configuration. The timescale of the thermalization is estimated to be $\sim 10^{3}-10^{4} \hbar /m_{e}c^{2}$.

astro-ph↗
arXiv2003

New perspectives in physics and astrophysics from the theoretical understanding of Gamma-Ray Bursts

If due attention is given in formulating the basic equations for the Gamma-Ray Burst (GRB) phenomenon and in performing the corresponding quantitative analysis, GRBs open a main avenue of inquiring on totally new physical and astrophysical regimes. This program is one of the greatest computational efforts in physics and astrophysics and cannot be actuated using shortcuts. A systematic approach has been highlighted in three paradigms: the relative space-time transformation (RSTT) paradigm, the interpretation of the burst structure (IBS) paradigm, the GRB-supernova time sequence (GSTS) paradigm. In fundamental physics new regimes are explored: (1) the process of energy extraction from black holes; (2) the quantum and general relativistic effects of matter-antimatter creation near the black hole horizon; (3) the physics of ultrarelativisitc shock waves with Lorentz gamma factor $γ> 100$. In astronomy and astrophysics also new regimes are explored: (i) the occurrence of gravitational collapse to a black hole from a critical mass core of mass $M\agt 10M_\odot$, which clearly differs from the values of the critical mass encountered in the study of stars ``catalyzed at the endpoint of thermonuclear evolution" (white dwarfs and neutron stars); (ii) the extremely high efficiency of the spherical collapse to a black hole, where almost 99.99% of the core mass collapses leaving negligible remnant; (iii) the necessity of developing a fine tuning in the final phases of thermonuclear evolution of the stars, both for the star collapsing to the black hole and the surrounding ones, in order to explain the possible occurrence of the "induced gravitational collapse". A new class of space missions to acquire information on such extreme new regimes are urgently needed.

astro-ph↗