17,052 research outputs found
A Brief Introduction to Loop Quantum Cosmology
In recent years, Loop Quantum Gravity has emerged as a solid candidate for a
nonperturbative quantum theory of General Relativity. It is a background
independent theory based on a description of the gravitational field in terms
of holonomies and fluxes. In order to discuss its physical implications, a lot
of attention has been paid to the application of the quantization techniques of
Loop Quantum Gravity to symmetry reduced models with cosmological solutions, a
line of research that has been called Loop Quantum Cosmology. We summarize its
fundamentals and the main differences with respect to the more conventional
quantization approaches employed in cosmology until now. In addition, we
comment on the most important results that have been obtained in Loop Quantum
Cosmology by analyzing simple homogeneous and isotropic models. These results
include the resolution of the classical big-bang singularity, which is replaced
by a quantum bounce.Comment: 15 pages, published in AIP Conference Proceedings, Volume 1130,
Geometry and Physics: XVII International Fall Workshop on Geometry and
Physic
Involutions on the Algebra of Physical Observables From Reality Conditions
Some aspects of the algebraic quantization programme proposed by Ashtekar are
revisited in this article. It is proved that, for systems with first-class
constraints, the involution introduced on the algebra of quantum operators via
reality conditions can never be projected unambiguously to the algebra of
physical observables, ie, of quantum observables modulo constraints. It is
nevertheless shown that, under sufficiently general assumptions, one can still
induce an involution on the algebra of physical observables from reality
conditions, though the involution obtained depends on the choice of particular
representatives for the equivalence classes of quantum observables and this
implies an additional ambiguity in the quantization procedure suggested by
Ashtekar.Comment: 19 pages, latex, no figure
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