Dirac Variables and Zero Modes of Gauss Constraint in Finite-Volume Two-Dimensional QED

The finite-volume QED$_{1+1}$ is formulated in terms of Dirac variables by an explicit solution of the Gauss constraint with possible nontrivial boundary conditions taken into account. The intrinsic nontrivial topology of the gauge group is thus revealed together with its zero-mode residual dynamics. Topologically nontrivial gauge transformations generate collective excitations of the gauge field above Coleman's ground state, that are completely decoupled from local dynamics, the latter being equivalent to a free massive scalar field theory.Comment: 13 pages, LaTe

The Ostrogradsky Method for Local Symmetries. Constrained Theories with Higher Derivatives

In the generalized Hamiltonian formalism by Dirac, the method of constructing the generator of local-symmetry transformations for systems with first- and second-class constraints (without restrictions on the algebra of constraints) is obtained from the requirement for them to map the solutions of the Hamiltonian equations of motion into the solutions of the same equations. It is proved that second-class constraints do not contribute to the transformation law of the local symmetry entirely stipulated by all the first-class constraints (and only by them). A mechanism of occurrence of higher derivatives of coordinates and group parameters in the symmetry transformation law in the Noether second theorem is elucidated. It is shown that the obtained transformations of symmetry are canonical in the extended (by Ostrogradsky) phase space. An application of the method in theories with higher derivatives is demonstrated with an example of the spinor Christ -- Lee model.Comment: 8 pages, LaTex; Talk given at the II International Workshop ``Classical and Quantum Integrable Systems'', Dubna, July 8-12, 1996; the essentially reduced version of the talk is published in Intern. J. Mod. Phys. A12, (1997)

Constrained Dynamical Systems: Separation of Constraints into First and Second Classes

In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are presented with the help of passing to an equivalent canonical set of constraints. The general structure of second-class constraints is clarified.Comment: 12 pages, LaTex; Preprint of Joint Institute for Nuclear Research E2-96-227, Dubna, 1996; to be published in Physical Review

Unconstrained Hamiltonian Formulation of SU(2) Gluodynamics

SU(2) Yang-Mills field theory is considered in the framework of the generalized Hamiltonian approach and the equivalent unconstrained system is obtained using the method of Hamiltonian reduction. A canonical transformation to a set of adapted coordinates is performed in terms of which the Abelianization of the Gauss law constraints reduces to an algebraic operation and the pure gauge degrees of freedom drop out from the Hamiltonian after projection onto the constraint shell. For the remaining gauge invariant fields two representations are introduced where the three fields which transform as scalars under spatial rotations are separated from the three rotational fields. An effective low energy nonlinear sigma model type Lagrangian is derived which out of the six physical fields involves only one of the three scalar fields and two rotational fields summarized in a unit vector. Its possible relation to the effective Lagrangian proposed recently by Faddeev and Niemi is discussed. Finally the unconstrained analog of the well-known nonnormalizable groundstate wave functional which solves the Schr\"odinger equation with zero energy is given and analysed in the strong coupling limit.Comment: 20 pages REVTEX, no figures; final version to appear in Phys. Rev. D; minor changes, notations simplifie