arXiv subjects

Philippe Droz-Vincent

Publications and source records attributed to Philippe Droz-Vincent.

11 recordsLinked to original sources

arXiv2016

Relativistic two-boson system in presence of electromagnetic plane waves

The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem involving five degrees of freedom.

hep-th↗

arXiv2014

Relative motion in spacetime

In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on the equal-time condition. The issue of an equivalent one-body description is discussed. We distinguish two different concepts: on the one hand an almost purely kinematic relative particle, on the other hand an effective particle which involves an explicit dynamical formulation; several versions of the latter are possible. Relative and effective particles have the same orbit, but may differ by their schedules.

physics.class-ph↗

arXiv2010

Hamiltonian two-body system in special relativity

We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on the equal-time condition. The center of mass is rather a center of energy. Individual energies are separately conserved and the meaning of their positivity is discussed in terms of world-lines. Several results derived decades ago under restrictive assumptions are extended to the general case. Relative motion has a structure similar to that of a nonrelativistic one-body motion in a stationnary external potential, but its evolution parameter is generally not a linear function of the center-of-mass time, unless the relative motion is circular (in this latter case the motion is periodic in the center-of-mass time). Finally the case of an extreme mass ratio is investigated. When this ratio tends to zero the heavy body coincides with the center of mass provided that a certain first integral, related to the binding energy is not too large.

math-ph↗

arXiv2009

Symmetries of the relativistic two-boson system in external field

We investigate the survival of symmetries in a relativistic system of two mutually interacting bosons coupled with an external field, when this field is "strongly" translation invariant in some directions and additionally remains unchanged by other isometries of spacetime. Since the relativistic interactions cannot be composed additively, it is not a priori garanteed that the two-body system inherits all the symmetries of the external potential. However, using an ansatz which permits to preserve the compatibility of the mass-shell constraints in the presence of the field, we show how "surviving isometries" can actually be implemented in the two-body wave equations.

hep-th↗

arXiv2007

Scalar products of elementary distributions

The field of real numbers being extended as a larger commutative field, we investigate the possibility of defining a scalar product for the distributions of finite discrete support. Then we focus on the most simple possible extension (which is an ordered field), we provide explicit formulas for this scalar product, and we exhibit a structure of positive definite inner-product space. In a one-dimensional application to the Schroedinger equation, the distributions supported by the origin are embedded into a bra-ket vector space, where the "singular" potential describing point interaction is defined in a natural way. A contact with the hyperreal numbers that arise in nonstandard analysis is possible but not essential, our extensions of $\bf R$ and $\bf C$ being obtained by a quite elementary method.

math-ph↗

arXiv2005

Covariant Model for Relativistic Three-Body Systems

The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These variables mix two-body clusters, which results in automatically incorporating three-body forces. Two superfluous degrees of freedom are eliminated, which yields a reduced equation for a wave function depending on three-dimensional arguments. When at least two masses are equal, this picture has a reasonable nonrelativistic limit. At first post-Galilean order and provided the interaction is not too much energy-dependent, the relativistic correction is tractable like a conventional perturbation problem. A covariant version of harmonic oscillator is given as a toy model.

hep-ph↗

arXiv2002

Invariant quantization in warped spacetimes

We argue that quantum theory in curved spacetime should be invariant under the continuous spacetime symmetries thaat are connected with the identity. For typical warped-product spacetimes, we prove that such invariance can be actually implemented, at least at the level of first quantization. Our approach rests on a mode decomposition which is special to the context of warped spacetimes.

gr-qc↗

arXiv2001

Binding Energy in Two and Three-Body Relativistic Dynamics

Two-body and three-body systems of scalar bosons are considered in the framework of covariant constraint dynamics. The reduced equation obtained after eliminating redundant degrees of freedom can be viewed as an eigenvalue equation for an observable which is intimately related with the relative motion. We display the connection of this observable with binding energy.

hep-th↗

arXiv2000

Mode solutions of the Klein-Gordon equation in warped spacetimes

In order to reduce the Klein-Gordon equation (with minimal coupling), we introduce a generalization of the so-called "mode solutions" that are well-known in the special case of a Robertson-Walker universe. After separation of the variables, we end up with a partial differential equation in lower dimension. A reduced version of the Gordon current arises and is conserved. When the first factor-manifold is Lorentzian, distinct modes appear as mutually orthogonal in the sense of the sesquilinear form obtained from the customary Gordon current. Moreover, a sesquilinear form is defined on the space of solutions to the reduced equation. Extension of this picture to curvature coupling is possible when the second factor-manifold has a constant scalar curvature.

gr-qc↗

arXiv1999

Two-Body Mass-Shell Constraints in a Constant Magnetic Field (Neutral Case)

A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a suitable representation. The relativistic symmetry associated with the magnetic field is carefully respected. Considering eigenstates of the pseudo momentum four-vector, we separate out collective variables and obtain a 3- dimensional reduced equation, posing a nonconventional eigenvalue problem. The velocity of the system as a whole generates "motional" terms in the formulas these terms are taken into account within a manifestly covariant framework.

hep-th↗

arXiv1998

Relativistic Quantum Mechanics of a Neutral Two-Body System in a Constant Magnetic Field

A (globally) neutral two-body system is supposed to obey a pair of coupled Klein-Gordon equations in a constant homogeneous magnetic field. Considering eigenstates of the pseudomomentum four-vector, we reduce these equations to a three-dimensional eigenvalue problem. The frame adapted to pseudomomentum has in general a nonvanishing velocity with respect to the frames where the field is purely magnetic. This velocity plays a crucial role in the occurance of motional terms; these terms are taken into account within a manifestly covariant framework. Perturbation theory is available when the mutual interaction doesnot depend on the total energy; a weak-field-slow-motion approximation is more specially tractable.

hep-th↗