289 research outputs found
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects
This is the first of a couple of papers in which, by exploiting the
capabilities of the Hamiltonian approach to general relativity, we get a number
of technical achievements that are instrumental both for a disclosure of
\emph{new} results concerning specific issues, and for new insights about
\emph{old} foundational problems of the theory. The first paper includes: 1) a
critical analysis of the various concepts of symmetry related to the
Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian
viewpoint, on the other. This analysis leads, in particular, to a
re-interpretation of {\it active} diffeomorphisms as {\it passive and
metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose the (nearly unknown) connection of
a subgroup of them to Hamiltonian gauge transformations {\it on-shell}; 2) a
re-visitation of the canonical reduction of the ADM formulation of general
relativity, with particular emphasis on the geometro-dynamical effects of the
gauge-fixing procedure, which amounts to the definition of a \emph{global
(non-inertial) space-time laboratory}. This analysis discloses the peculiar
\emph{dynamical nature} that the traditional definition of distant simultaneity
and clock-synchronization assume in general relativity, as well as the {\it
gauge relatedness} of the "conventions" which generalize the classical
Einstein's convention.Comment: 45 pages, Revtex4, some refinements adde
New Directions in Non-Relativistic and Relativistic Rotational and Multipole Kinematics for N-Body and Continuous Systems
In non-relativistic mechanics the center of mass of an isolated system is
easily separated out from the relative variables. For a N-body system these
latter are usually described by a set of Jacobi normal coordinates, based on
the clustering of the centers of mass of sub-clusters. The Jacobi variables are
then the starting point for separating {\it orientational} variables, connected
with the angular momentum constants of motion, from {\it shape} (or {\it
vibrational}) variables. Jacobi variables, however, cannot be extended to
special relativity. We show by group-theoretical methods that two new sets of
relative variables can be defined in terms of a {\it clustering of the angular
momenta of sub-clusters} and directly related to the so-called {\it dynamical
body frames} and {\it canonical spin bases}. The underlying group-theoretical
structure allows a direct extension of such notions from a non-relativistic to
a special- relativistic context if one exploits the {\it rest-frame instant
form of dynamics}. The various known definitions of relativistic center of mass
are recovered. The separation of suitable relative variables from the so-called
{\it canonical internal} center of mass leads to the correct kinematical
framework for the relativistic theory of the orbits for a N-body system with
action -at-a-distance interactions. The rest-frame instant form is also shown
to be the correct kinematical framework for introducing the Dixon multi-poles
for closed and open N-body systems, as well as for continuous systems,
exemplified here by the configurations of the Klein-Gordon field that are
compatible with the previous notions of center of mass.Comment: Latex, p.75, Invited contribution for the book {\it Atomic and
Molecular Clusters: New Research} (Nova Science
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time
(abridged)The achievements of the present work include: a) A clarification of
the multiple definition given by Bergmann of the concept of {\it (Bergmann)
observable. This clarification leads to the proposal of a {\it main conjecture}
asserting the existence of i) special Dirac's observables which are also
Bergmann's observables, ii) gauge variables that are coordinate independent
(namely they behave like the tetradic scalar fields of the Newman-Penrose
formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict
connection with the Hamiltonian treatment of the initial value problem in
metric gravity for the class of Christoudoulou -Klainermann space-times, in
which the temporal evolution is ruled by the {\it weak} ADM energy. It is
crucial the re-interpretation of {\it active} diffeomorphisms as {\it passive
and metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose their (nearly unknown) connection
to gauge transformations on-shell; this is expounded in the first paper
(gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsic
pseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinate
systems for the 4-dimensional {\it mathematical} manifold, in terms of the
highly non-local degrees of freedom of the gravitational field (its four
independent {\it Dirac observables}), and to realize the {\it physical
individuation} of the points of space-time as {\it point-events} as a
gauge-fixing problem, also associating a non-commutative structure to each
4-coordinate system.Comment: 41 pages, Revtex
Dynamical Body Frames, Orientation-Shape Variables and Canonical Spin Bases for the Non-Relativistic N-Body Problem
After the separation of the center-of-mass motion, a new privileged class of canonical Darboux bases is proposed for the non-relativistic N-body problem by exploiting a geometrical and group theoretical approach to the definition of {\it body frame} for deformable bodies. This basis is adapted to the rotation group SO(3), whose canonical realization is associated with a symmetry Hamiltonian {\it left action}. The analysis of the SO(3) coadjoint orbits contained in the N-body phase space implies the existence of a {\it spin frame} for the N-body system. Then, the existence of appropriate non-symmetry Hamiltonian {\it right actions} for non-rigid systems leads to the construction of a N-dependent discrete number of {\it dynamical body frames} for the N-body system, hence to the associated notions of {\it dynamical} and {\it measurable} orientation and shape variables, angular velocity, rotational and vibrational configurations. For N=3 the dynamical body frame turns out to be unique and our approach reproduces the {\it xxzz gauge} of the gauge theory associated with the {\it orientation-shape} SO(3) principal bundle approach of Littlejohn and Reinsch. For our description is different, since the dynamical body frames turn out to be {\it momentum dependent}. The resulting Darboux bases for are connected to the coupling of the {\it spins} of particle clusters rather than the coupling of the {\it centers of mass} (based on Jacobi relative normal coordinates). One of the advantages of the spin coupling is that, unlike the center-of-mass coupling, it admits a relativistic generalization
Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators
The possible external couplings of an extended non-relativistic classical
system are characterized by gauging its maximal dynamical symmetry group at the
center-of-mass. The Galilean one-time and two-times harmonic oscillators are
exploited as models. The following remarkable results are then obtained: 1) a
peculiar form of interaction of the system as a whole with the external gauge
fields; 2) a modification of the dynamical part of the symmetry
transformations, which is needed to take into account the alteration of the
dynamics itself, induced by the {\it gauge} fields. In particular, the
Yang-Mills fields associated to the internal rotations have the effect of
modifying the time derivative of the internal variables in a scheme of minimal
coupling (introduction of an internal covariant derivative); 3) given their
dynamical effect, the Yang-Mills fields associated to the internal rotations
apparently define a sort of Galilean spin connection, while the Yang-Mills
fields associated to the quadrupole momentum and to the internal energy have
the effect of introducing a sort of dynamically induced internal metric in the
relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty
available at: http://www.iop.org/). The file is available at:
http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip
file with the IOP preprint style include
An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity
In this paper we treat the so called clock paradox in an analytical way by
assuming that a constant and uniform force F of finite magnitude acts
continuously on the moving clock along the direction of its motion assumed to
be rectilinear. No inertial motion steps are considered. The rest clock is
denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which
(1) is at rest in its origin and (2) is seen moving is I and, finally, the
accelerated frame in which (2) is at rest in its origin and (1) moves forward
and backward is A. We deal with the following questions: I) What is the effect
of the finite force acting on (2) on the proper time intervals measured by the
two clocks when they reunite? Does a differential aging between the two clocks
occur, as it happens when inertial motion and infinite values of the
accelerating force is considered? The Special Theory of Relativity is used in
order to describe the hyperbolic motion of (2) in the frame I II) Is this
effect an absolute one, i.e. does the accelerated observer A comoving with (2)
obtain the same results as that in I, both qualitatively and quantitatively, as
it is expected? We use the General Theory of Relativity in order to answer this
question.Comment: LaTex2e, 19 pages, no tables, no figures. Rewritten version, it
amends the previous one whose results about the treatment with General
Relativity were wrong. References added. Eq. (55) corrected. More refined
version. Comments and suggestions are warmly welcom
Multipolar Expansions for the Relativistic N-Body Problem in the Rest-Frame Instant Form
Dixon's multipoles for a system of N relativistic positive-energy scalar
particles are evaluated in the rest-frame instant form of dynamics. The Wigner
hyperplanes (intrinsic rest frame of the isolated system) turn out to be the
natural framework for describing multipole kinematics. In particular, concepts
like the {\it barycentric tensor of inertia} can be defined in special
relativity only by means of the quadrupole moments of the isolated system.Comment: 46 pages, revtex fil
Locality hypothesis and the speed of light
The locality hypothesis is generally considered necessary for the study of
the kinematics of non-inertial systems in special relativity. In this paper we
discuss this hypothesis, showing the necessity of an improvement, in order to
get a more clear understanding of the various concepts involved, like
coordinate velocity and standard velocity of light. Concrete examples are
shown, where these concepts are discussed.Comment: 23 page
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