BRST formalism for systems with higher order derivatives of gauge parameters

For a wide class of mechanical systems, invariant under gauge transformations with higher (arbitrary) order time derivatives of gauge parameters, the equivalence of Lagrangian and Hamiltonian BRST formalisms is proved. It is shown that the Ostrogradsky formalism establishes the natural rules to relate the BFV ghost canonical pairs with the ghosts and antighosts introduced by the Lagrangian approach. Explicit relation between corresponding gauge-fixing terms is obtained.Comment: 19 pages, LaTeX, no figure

Toda equations associated with loop groups of complex classical Lie groups

A Toda equation is specified by a choice of a Lie group and a $\mathbb Z$-gradation of its Lie algebra. The Toda equations associated with loop groups of complex classical Lie groups, whose Lie algebras are endowed with integrable $\mathbb Z$-gradations with finite dimensional grading subspaces, are described in an explicit form.Comment: 39 page

The Ostrogradsky prescription for BFV formalism

Gauge-invariant systems of a general form with higher order derivatives of gauge parameters are investigated within the framework of the BFV formalism. Higher order terms of the BRST charge and BRST-invariant Hamiltonian are obtained. It is shown that the identification rules for Lagrangian and Hamiltonian ghost variables depend on the choice of the extension of constraints from the primary constraint surface.Comment: LaTeX, 13 page

Solving non-abelian loop Toda equations

We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation suggested by the initial \bbZ-gradation.Comment: 28 page

Pseudoclassical model for topologically massive gauge fields

A pseudoclassical model for P,T-invariant system of topologically massive U(1) gauge fields is analyzed. The model demonstrates a nontrivial relationship between continuous and discrete symmetries and reveals a phenomenon of ``classical quantization''. It allows one to identify SU(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. We show this P,T-invariant quantum system realizes an irreducible representation of a non-standard super-extension of the (2+1)-dimensional Poincare group.Comment: 10 pages, LaTeX, no figures; titles for sections and keywords added, refs update