79 research outputs found
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 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
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