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Luca Lusanna

Publications and source records attributed to Luca Lusanna.

71 records · Page 4Linked to original sources
arXiv2000

The Rest-Frame Darwin Potential from the Lienard-Wiechert Solution in the Radiation Gauge

In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables ($Q_i^2=0, Q_iQ_j\ne 0$), it is possible to re-express the Lienard-Wiechert potentials and electric fields in the radiation gauge as phase space functions, because the difference among retarded, advanced, and symmetric Green functions is of order Q_i^2. By working in the rest-frame instant form of dynamics, the elimination of the electromagnetic degrees of freedom by means of suitable second classs contraints leads to the identification of the Lienard-Wiechert reduced phase space containing only N charged particles with mutual action-at-a-distance vector and scalar potentials. A Darboux canonical basis of the reduced phase space is found. This allows one to re-express the potentials for arbitrary N as a unique effective scalar potential containing the Coulomb potential and the complete Darwin one, whose 1/c^2 component agrees for with the known expression. The effective potential gives the classical analogue of all static and non-static effects of the one-photon exchange Feynman diagram of scalar electrodynamics.

hep-th↗
arXiv1999

Tetrad Gravity: III) Asymptotic Poincare' Charges, the Physical Hamiltonian and Void Spacetimes

A discussion of asymptotic weak and strong Poincare' charges in metric gravity is given to identify the proper Hamiltonian boundary conditions. The asymptotic part of the lapse and shift functions is put equal to their analogues on Minkowski hyperplanes. By adding Dirac's ten extra variables at spatial infinity, metric gravity is extended to incorporate Dirac's ten extra first class constraints (the new ten momenta equal to the weak Poincare' charges) and this allows its deparametrization to parametrized Minkowski theories restricted to spacelike hyperplanes. The absence of supertranslations implies: i) boundary conditions identifying the family of Christodoulou-Klainermann spacetimes; ii) the restriction of foliations to those (Wigner-Sen-Witten hypersurfaces) corresponding to Wigner's hyperplanes of Minkowski rest-frame instant form. These results are generalized to tetrad gravity in the new formulation given in gr-qc/9807072, gr-qc/9807073. The evolution in the parameter labelling the leaves of the foliation is generated by the weak ADM energy. Some comments on the quantization in a completely fixed special 3-orthogonal gauge are made.

gr-qc↗
arXiv1999

Tetrad Gravity: I) A New Formulation

A new version of tetrad gravity in globally hyperbolic, asymptotically flat at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is obtained by using a new parametrization of arbitrary cotetrads to define a set of configurational variables to be used in the ADM metric action. Seven of the fourteen first class constraints have the form of the vanishing of canonical momenta. A comparison is made with other models of tetrad gravity and with the ADM canonical formalism for metric gravity. The phase space expression of various 4-tensors is explicitly given.

gr-qc↗
arXiv1999

Tetrad Gravity: II) Dirac's Observables

After a study of the Hamiltonian group of gauge transformations of canonical tetrad gravity on globally hyperbolic, asymptotically flat at spatial infinity, spacetimes with Cauchy hypersurfaces $Σ_τ$ diffeomorphic to $R^3, we find the dependence of the cotriads on $Σ_τ$ and of their momenta on the six parameters associated with rotations and space diffeomorphisms. The choice of 3-coordinates on $Σ_τ$ is equivalent to the parametrization of the cotriads with the last three degrees of freedom individuating the 3-geometries. The Shanmugadhasan canonical transformation, corresponding to the choice of 3-orthogonal coordinates on $Σ_τ$ and adapted to 13 of the 14 first class constraints, and the interpretation of the gauge transformations are given. The gauge interpretation of tetrad gravity based on constraint theory implies that a "Hamiltonian kinematical gravitational field" is an equivalence class of pseudo-Riemannian spacetimes modulo the Hamiltonian group of gauge transformations: it includes a conformal 3-geometry and all the different 4-geometries (standard definition of a kinematical gravitational field, $Riem M^4/Diff M^4$) connected to it by the gauge transformations. A "Hamiltonian Einstein or dynamical gravitational field" is a kinematical one which satisfies the Hamilton-Dirac equations generated by the ADM energy: it coincides with the standard Einstein or dynamical gravitational field, namely a 4-geometry solution of Einstein's equations, since the Hilbert and ADM actions both generate Einstein's equations so that the kinematical Hamiltonian gauge transformations are dynamically restricted to the spacetime diffeomorphisms of the solutions of Einstein's equations.

gr-qc↗
arXiv1997

The Lienard-Wiechert Potential of Charged Scalar Particles and their Relation to Scalar Electrodynamics in the Rest-Frame Instant Form

After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar particles with pseudoclassical Grassmann-valued electric charges plus the electromagnetic field are studied. The Lienard-Wiechert potentials of the particles are evaluated and it is shown how the causality problems of the Abraham-Lorentz-Dirac equation are solved at the pseudoclassical level. Then, the covariant rest-frame description of scalar electrodynamics is given. Applying to it the Feshbach-Villars formalism, the connection with the particle plus electromagnetic field system is found.

hep-th↗
arXiv1997

The Classical Relativistic Quark Model in the Rest-Frame Wigner-Covariant Coulomb Gauge

The system of N scalar particles with Grassmann-valued color charges plus the color SU(3) Yang-Mills field is reformulated on spacelike hypersurfaces. The Dirac observables are found and the physical invariant mass of the system in the Wigner-covariant rest-frame instant form of dynamics (covariant Coulomb gauge) is given. From the reduced Hamilton equations we extract the second order equations of motion both for the reduced transverse color field and the particles. Then, we study this relativistic scalar quark model, deduced from the classical QCD Lagrangian and with the color field present, in the N=2 (meson) case. A special form of the requirement of having only color singlets, suited for a field-independent quark model, produces a ``pseudoclassical asymptotic freedom" and a regularization of the quark self-energy.

hep-th↗
arXiv1996

Dirac's Observables for the Higgs Model: I) the Abelian Case

We search a canonical basis of Dirac's observables for the classical Abelian Higgs model with fermions in the case of a trivial U(1) principal bundle. The study of the Gauss law first class constraint shows that the model has two disjoint sectors of solutions associated with two physically different phases. In the electromagnetic phase, the electromagnetic field remains massless: after the determination of the Dirac's observables we get that both the reduced physical Hamiltonian and Lagrangian are nonlocal. In the Higgs phase, the electromagnetic field becomes massive and in terms of Dirac's observables we get a local, but nonanalytic in the electric charge (or equivalently in the sum of the electromagnetic mass and of the residual Higgs field), physical Hamiltonian; however the associated Lagrangian is nonlocal. Some comments on the R-gauge-fixing, the possible elimination of the residual Higgs field and on the Nielsen-Olesen vortex solution close the paper.

hep-th↗
arXiv1996

Dirac's Observables for the Higgs Model: II) the non-Abelian SU(2) Case

We search a canonical basis of Dirac's observables for the classical non-Abelian Higgs model with fermions in the case of a trivial SU(2) principal bundle with a complex doublet of Higgs fields and with the fermions in a given representation of SU(2). Since each one of the three Gauss law first class constraints can be solved either in the corresponding longitudinal electric field or in the corresponding Higgs momentum, we get a priori eight disjoint phases of solutions of the model. The only two phases with SU(2) covariance are the SU(2) phase with massless SU(2) fields and the Higgs phase with massive SU(2) fields. The Dirac observables and the reduced physical (local) Hamiltonian and (nonlocal) Lagrangian of the Higgs phase are evaluated: the main result is the nonanalyticity in the SU(2) coupling constant, or equivalently in the sum of the residual Higgs field and of the mass of the SU(2) fields. Some comments on the function spaces needed for the gauge fields are made.

hep-th↗
arXiv1995

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.

hep-th↗
arXiv1995

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 to

hep-th↗
arXiv1994

Dirac's Observables for Yang-Mills Theory with Fermions

A canonical basis of global Dirac's observables for Yang-Mills theory with fermions are obtained in a functional space in which Gribov ambiguity is absent and Gauss' laws can be solved exactly. In terms of these observables, one can express the Lagrangian, the Hamiltonian, non-Abelian and topological charges. The problem of the covariantization of these non-local and non-polynomial quantities is solved. From a relativistic presymplectic approach to the localization of the relativistic center-of-mass of the field configuration, a ultraviolet cutoff is deduced.

hep-th↗