Relativistic Equations of Motion within Nambu's Formalism of Dynamics

✍ Scribed by R.M. Yamaleev

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 172 KB
• Volume: 285
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2000.6075

✦ Synopsis

The equations of motion for the relativistic particle in an external electromagnetic field are reformulated within the framework of the Nambu three-order phase space formalism. This formulation implies the mass of a relativistic particle as an integral of motion. The Lorentzcovariant four-vector of momentum is decomposed into two four-dimensional euclidean vectors forming the coordinates of the three-order phase space formalism. The new set of equations of motion describing the motion of a relativistic charged spinning particle in interaction with an external electromagnetic field is given in terms of quaternions. These equations give rise to Lorentz-force equations with no auxiliary conditions.

2000 Academic Press Recently [12], we proposed an extension of Newtonian mechanics in (D 3)dimensional phase space within Nambu's formalism. As a consequence, a correspondence between the generalized Newtonian equations and the relativistic equations of motion has been established. However, this correspondence was found only for the case of one-dimensional motion in a stationary potential. In this paper we generalize this result to the case of three-dimensional coordinate space for a relativistic charged spinning particle in interaction with an external electromagnetic