135 research outputs found

### Canonical Reduction of Gravity: from General Covariance to Dirac Observables and post-Minkowskian Background-Independent Gravitational Waves

The status of canonical reduction for metric and tetrad gravity in
space-times of the Christodoulou-Klainermann type, where the ADM energy rules
the time evolution, is reviewed. Since in these space-times there is an
asymptotic Minkowski metric at spatial infinity, it is possible to define a
Hamiltonian linearization in a completely fixed (non harmonic) 3-orthogonal
gauge without introducing a background metric. Post-Minkowskian
background-independent gravitational waves are obtained as solutions of the
linearized Hamilton equations.Comment: 9 pages, Talk given at the Symposium QTS3 on Quantum Theory and
Symmetries, Cincinnati, September, 10-14 200

### N- and 1-time Classical Description of N-body Relativistic Kinematics and the Electromagnetic Interaction

The intrinsic covariant 1-time description (rest-frame instant form) for N
relativistic scalar particles is defined. The system of N charged scalar
particles plus the electromagnetic field is described in this way: the study of
its Dirac observables allows the extraction of the Coulomb potential from field
theory and the regularization of the classical self-energy by using
Grassmann-valued electric charges. The 1-time covariant relativistic
statistical mechanics is defined

### On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

The four (electro-magnetic, weak, strong and gravitational) interactions are
described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian
constraints. As a consequence a subset of the original configuration variables
are {\it gauge variables}, not determined by the equations of motion. Only at
the Hamiltonian level it is possible to separate the gauge variables from the
deterministic physical degrees of freedom, the {\it Dirac observables}, and to
formulate a well posed Cauchy problem for them both in special and general
relativity. Then the requirement of {\it causality} dictates the choice of {\it
retarded} solutions at the classical level. However both the problems of the
classical theory of the electron, leading to the choice of ${1\over 2}
(retarded + advanced)$ solutions, and the regularization of quantum field
teory, leading to the Feynman propagator, introduce {\it anticipatory} aspects.
The determination of the relativistic Darwin potential as a semi-classical
approximation to the Lienard-Wiechert solution for particles with
Grassmann-valued electric charges, regularizing the Coulomb self-energies,
shows that these anticipatory effects live beyond the semi-classical
approximation (tree level) under the form of radiative corrections, at least
for the electro-magnetic interaction.Comment: 12 pages, Talk and "best contribution" at The Sixth International
Conference on Computing Anticipatory Systems CASYS'03, Liege August 11-16,
200

### Aspects of Galilean and Relativistic Particle Mechanics with Dirac's Constraints

Relevant physical models are described by singular Lagrangians, so that their
Hamiltonian description is based on the Dirac theory of constraints. The
qualitative aspects of this theory are now understood, in particular the role
of the Shanmugadhasan canonical transformation in the determination of a
canonical basis of Dirac's observables allowing the elimination of gauge
degrees of freedom from the classical description of physical systems. This
programme was initiated by Dirac for the electromagnetic field with charged
fermions. Now Dirac's observables for Yang-Mills theory with fermions (whose
typical application is QCD) have been found in suitable function spaces where
the Gribov ambiguity is absent. Also the ones for the Abelian Higgs model are
known and those for the $SU(2) \times U(1)$ electroweak theory with fermions
are going to be found with the same method working for the Abelian case. The
main task along these lines will now be the search of Dirac's observables for
tetrad gravity in the case of asymptotically flat 3-manifolds. The philosophy
behind this approach is ``first reduce, then quantize": this requires a global
symplectic separation of the physical variables from the gauge ones so that the
role of differential geometry applied to smooth field configurations is
dominating, in contrast with the standard approach of ``first quantizing, then
reducing", where, in the case of gauge field theory, the reduction process
takes place on distributional field configurations, which dominate in quantum
measures. This global separation has been accomplished till now, at least at a
heuristic level, and one is going to have a classical (pseudoclassical for the
fermion) variables basis for the physical description of the $SU(3)\times
SU(2)\times U(1)$ standard model; instead, with tetrad gravity one expects toComment: Talk given at the Conference ``Theories of Fundamental Interactions",
Maynooth (Ireland), May 1995. (LaTeX file

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