Canonical formalism for quasi-classical particle “Zitterbewegung” in Ostrohrads’kyj mechanics. (English) Zbl 1329.70043

Matsyuk, Roman

Bureš, Jarolím (ed.) et al., Differential geometry and its applications. Proceedings of the 9th international conference on differential geometry and its applications, DGA 2004, Prague, Czech Republic, August 30–September 3, 2004. Prague: matfyzpress (ISBN 80-86732-63-0/pbk). 629-637 (2005).

Summary: The homogeneous canonical formalism of Rund is applied to the second-order Lagrangian model of the self-interacting particle of Bopp. The quasi-classical free spinning particle of Mathisson appears then as a constrained subsystem of the previous system. Differential-geometric mechanisms offered in this work are formulated in a fairy general manner, although revealed here in a particular example of physical meaning.
For the entire collection see [Zbl 1097.53001].

MSC:

70H03	Lagrange’s equations
70G45	Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70H50	Higher-order theories for problems in Hamiltonian and Lagrangian mechanics