Dynamical sectors of a relativistic two particle model

Abstract

We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom. The presence or absence of sectors depends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.

Chern–Simons-Like Gravity Theories

“…In general, the functionals φ [ξ ] will not be differentiable, but we can make them so by adding boundary terms. Varying (10) with respect to the fields a i s gives…”

“…This problem appears to be distinct from the problem of whether the "Dirac conjecture" is satisfied, since that concerns the values of Lagrange multipliers of first-class constraints. It may be related to the recently discussed "sectors" issue[10].…”

Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework

“…In the present paper, we have used the Faddeev-Jackiw symplectic approach to analyze the dynamical structure of two interacting relativistic particles [22], which can also be interpreted as a bigravity model in one dimension. One of the interesting features of this analysis is the fact that the dynamical content of this model has been extracted by studying only the properties of the symplectic matrix and its corresponding zero-modes.…”

“…In a recent paper [22], in order to have a better understanding of how to deal with this kind of dynamical systems, a simple model was considered that describes two relativistic particles with interaction [23,24], which possesses many interesting properties since this model can be interpreted as a bigravity model in one dimension. The primary, secondary, tertiary and quaternary constraints were derived [22] by using Dirac's Hamiltonian formalism. However, it turns out that the procedure for separating the second-class from the first-class constraints is not completely clear.…”

“…The aim of the present paper is to study this problem in an alternative approach from the one presented in Ref. [22]. In particular, we will apply the symplectic approach developed by Faddeev and Jackiw [25].…”