Ip. Pavlotsky et M. Strianese, SOME PECULIAR PROPERTIES OF THE DARWIN LAGRANGIAN, International journal of modern physics b, 9(23), 1995, pp. 3069-3083
In the post-Galilean approximation the Lagrangians are singular on a s
ubmanifold of the phase space. It is a local singularity, which differ
s from the ones considered by Dirac. The dynamical properties are esse
ntially peculiar on the studied singular surfaces. In the preceding pu
blications,(1'2'3) two models of singular relativistic Lagrangians and
the rectilinear motion of two electrons, determined by Darwin's Lagra
ngian, were examined. In the present paper we study the peculiar dynam
ical properties of the two-dimensional Darwin's Lagrangian. In particu
lar, it is shown that the minimal distance between two electrons (the
so called ''radius of electron'') appears in the two-dimensional motio
n as well as in one-dimensional case. Some new peculiar properties are
discovered.