Description of Friedmann Observables in Quantum Universe

The solution of the problem of describing the Friedmann observables (the Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis of the method of gaugeless Hamiltonian reduction in which the gravitational part of the energy constraint is considered as a new momentum. We show that the conjugate variable corresponding to the new momentum plays a role of the invariant time parameter of evolution of dynamical variables in the sector of the Dirac observables of the general Hamiltonian approach. Relations between these Dirac observables and the Friedmann observables of the expanding Universe are established for the standard Friedmann cosmological model with dust and radiation. The presented reduction removes an infinite factor from the functional integral, provides the normalizability of the wave function of the Universe and distinguishes the conformal frame of reference where the Hubble law is caused by the alteration of the conformal dust mass.Comment: 10 pages, LaTe

The BMS/GCA correspondence

We find a surprising connection between asymptotically flat space-times and non-relativistic conformal systems in one lower dimension. The BMS group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean Conformal Algebra which is of relevance to non-relativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit of a radially infalling null ray inspired by non-relativistic scaling and obtain a flat metric. The 4D BMS algebra is also discussed and found to be the same as another class of GCA, called the semi-GCA, in three dimensions. We propose a general BMS/GCA correspondence. Some consequences are discussed.Comment: 17 page

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