365 research outputs found
Dynamics of Scalar Field in Polymer-like Representation
In recent twenty years, loop quantum gravity, a background independent
approach to unify general relativity and quantum mechanics, has been widely
investigated. We consider the quantum dynamics of a real massless scalar field
coupled to gravity in this framework. A Hamiltonian operator for the scalar
field can be well defined in the coupled diffeomorphism invariant Hilbert
space, which is both self-adjoint and positive. On the other hand, the
Hamiltonian constraint operator for the scalar field coupled to gravity can be
well defined in the coupled kinematical Hilbert space. There are 1-parameter
ambiguities due to scalar field in the construction of both operators. The
results heighten our confidence that there is no divergence within this
background independent and diffeomorphism invariant quantization approach of
matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the
master constraint programme can be carried out in this coupled system by
employing a self-adjoint master constraint operator on the diffeomorphism
invariant Hilbert space.Comment: 24 pages, accepted for pubilcation in Class. Quant. Gra
The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology
This letter is motivated by the recent papers by Dittrich and Thiemann and,
respectively, by Rovelli discussing the status of Quantum Geometry in the
dynamical sector of Loop Quantum Gravity. Since the papers consider model
examples, we also study the issue in the case of an example, namely on the Loop
Quantum Cosmology model of space-isotropic universe. We derive the
Rovelli-Thiemann-Ditrich partial observables corresponding to the quantum
geometry operators of LQC in both Hilbert spaces: the kinematical one and,
respectively, the physical Hilbert space of solutions to the quantum
constraints. We find, that Quantum Geometry can be used to characterize the
physical solutions, and the operators of quantum geometry preserve many of
their kinematical properties.Comment: Latex, 12 page
Master Constraint Operator in Loop Quantum Gravity
We introduce a master constraint operator densely defined
in the diffeomorphism invariant Hilbert space in loop quantum gravity, which
corresponds classically to the master constraint in the programme. It is shown
that is positive and symmetric, and hence has its Friedrichs
self-adjoint extension. The same conclusion is tenable for an alternative
master operator , whose quadratic form coincides with the
one proposed by Thiemann. So the master constraint programme for loop quantum
gravity can be carried out in principle by employing either of the two
operators.Comment: 11 pages, significant modification in section 2, accepted for
publication in Phys. Lett.
The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity
The role of fermionic matter in the spectrum of the area operator is analyzed
using the Baez--Krasnov framework for quantum fermions and gravity. The result
is that the fermionic contribution to the area of a surface is equivalent
to the contribution of purely gravitational spin network's edges tangent to
. Therefore, the spectrum of the area operator is the same as in the pure
gravity case.Comment: 10 pages, revtex file. Revised versio
Exploring the diffeomorphism invariant Hilbert space of a scalar field
As a toy model for the implementation of the diffeomorphism constraint, the
interpretation of the resulting states, and the treatment of ordering
ambiguities in loop quantum gravity, we consider the Hilbert space of spatially
diffeomorphism invariant states for a scalar field. We give a very explicit
formula for the scalar product on this space, and discuss its structure.
Then we turn to the quantization of a certain class of diffeomorphism
invariant quantities on that space, and discuss in detail the ordering issues
involved. On a technical level these issues bear some similarity to those
encountered in full loop quantum gravity.Comment: 20 pages, no figures; v3: corrected typos, added reference, some
clarifications added; version as published in CQ
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