Auxiliary representations of Lie algebras and the BRST constructions

The method of construction of auxiliary representations for a given Lie algebra is discussed in the framework of the BRST approach. The corresponding BRST charge turns out to be non -- hermitian. This problem is solved by the introduction of the additional kernel operator in the definition of the scalar product in the Fock space. The existence of the kernel operator is proven for any Lie algebra.Comment: 11 pages, LaTe

Nonlinear Realizations of Superconformal Groups and Spinning Particles

The method of nonlinear realizations is applied for the conformally invariant description of the spinning particles in terms of geometrical quantities of the parameter spaces of the one dimensional N - extended superconformal groups. We develop the superspace approach to the cases of spin 0, 1/2, 1 particles and describe the alternative component approach in the application to the spin-1/2 particle.Comment: 8 pages, Latex, style file espcrc2.sty. Talk given at the D.V. Volkov Memorial Conference ``Supersymmetry and Quantum Field Theory'', July 25-30, 2000, Kharkov, to be published in the Nuclear Physics B Conference Supplement

On the consistency of the Horava Theory

With the goal of giving evidence for the theoretical consistency of the Horava Theory, we perform a Hamiltonian analysis on a classical model suitable for analyzing its effective dynamics at large distances. The model is the lowest-order truncation of the Horava Theory with the detailed-balance condition. We consider the pure gravitational theory without matter sources. The model has the same potential term of general relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant lambda. Since this constant breaks the general covariance under space-time diffeomorphisms, it is believed that arbitrary values of lambda deviate the model from general relativity. We show that this model is not a deviation at all, instead it is completely equivalent to general relativity in a particular partial gauge fixing for it. In doing this, we clarify the role of a second-class constraint of the model.Comment: The wording has been revised in general, specially in abstract, introduction and conclusions. No changes in results. Version published in IJMP

The lagrangian description of representations of the Poincare group

The construction of lagrangians describing the various representations of the Poincare group is given in terms of the BRST approach.Comment: 8 pages, Latex, style file espcrc2.sty. Talk given at the D.V. Volkov Memorial Conference ``Supersymmetry and Quantum Field Theory'', July 25-30, 2000, Kharkov, to be published in the Nuclear Physics B Conference Supplement

Reparametrization Invariance and the Schr\"odinger Equation

In the present work we consider a time-dependent Schr\"odinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schr\"odinger equation. The procedure is applicable in the supersymmetric theories as well. The $n=2$ supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schr\"odinger equation.Comment: RevTeX,25 page