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Ph. Droz-Vincent

Publications and source records attributed to Ph. Droz-Vincent.

5 recordsLinked to original sources
arXiv2006

Relativistic Corrections in a Three-Boson System of Equal Masses

Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the mass-shell constraints can be reduced to a three-dimensional eigenvalue problem. In general, this problem is complicated, but for three equal masses a drastic simplification arises at the first post-Galilean order: the reduced wave equation becomes tractable, and we can compute a first-order correction beyond the nonrelativistic limit. The harmonic interaction is displayed as a toy model.

hep-th↗
arXiv2003

Reduction of relativistic three-body kinematics

The Klein-Gordon system describing three scalar particles without interaction is cast into a new form, by transformation of the momenta. Two redundant degrees of freedom are eliminated; we are left with a covariant equation for a reduced wave function with three-dimensional arguments. This new formulation of the mass-shell constraints is equivalent to the original KG system in a sector characterized by positivity of the energies and, if the mass differences are not too large, by a moderately relativistic regime. Then, mutual interaction is introduced and produces a tractable model.

hep-th↗
arXiv1998

Invariance of Positive-Frequency Kernels in Generalized FRW Spacetimes

We consider the Klein-Gordon equation in FRW-like spacetimes, with compact space sections (not necessarily isotropic neither homogeneous). The bi-scalar kernel allowing to select the positive-frequency part of any solution is developed on mode solutions, using the eigenfunctions of the three-dimensional Laplacian. Of course this kernel is not unique but, except (perhaps) when the scale factor undergoes a special law of evolution, the metric has no more symmetries (connected with the identity) than those inherited from the space sections. As a result, all admissible definitions of the positive-frequency kernel are related one to another by a unitary transformation which commutes with the connected isometries of spacetime; any such kernel is invariant under these isometries isometries. A physical interpretation is tentatively suggested.

gr-qc↗
arXiv1996

Direct Interactions in Relativistic Statistical Mechanics

Directly interacting particles are considered in the multitime formalism of predictive relativistic mechanics. When the equations of motion leave a phase-space volume invariant, it turns out that the phase average of any first integral, covariantly defined as a flux across a $7n$-dimensional surface, is conserved. The Hamiltonian case is discussed, a class of simple models is exhibited, and a tentative definition of equilibrium is proposed.

hep-th↗