4 research outputs found
Refined algebraic quantisation with the triangular subgroup of SL(2,R)
We investigate refined algebraic quantisation with group averaging in a
constrained Hamiltonian system whose gauge group is the connected component of
the lower triangular subgroup of SL(2,R). The unreduced phase space is
T^*R^{p+q} with p>0 and q>0, and the system has a distinguished classical
o(p,q) observable algebra. Group averaging with the geometric average of the
right and left invariant measures, invariant under the group inverse, yields a
Hilbert space that carries a maximally degenerate principal unitary series
representation of O(p,q). The representation is nontrivial iff (p,q) is not
(1,1), which is also the condition for the classical reduced phase space to be
a symplectic manifold up to a singular subset of measure zero. We present a
detailed comparison to an algebraic quantisation that imposes the constraints
in the sense H_a Psi = 0 and postulates self-adjointness of the o(p,q)
observables. Under certain technical assumptions that parallel those of the
group averaging theory, this algebraic quantisation gives no quantum theory
when (p,q) = (1,2) or (2,1), or when p>1, q>1 and p+q is odd.Comment: 30 pages. LaTeX with amsfonts, amsmath, amssymb. (v4: Typos
corrected. Published version.
Dynamical Vacuum in Quantum Cosmology
By regarding the vacuum as a perfect fluid with equation of state p=-rho, de
Sitter's cosmological model is quantized. Our treatment differs from previous
ones in that it endows the vacuum with dynamical degrees of freedom. Instead of
being postulated from the start, the cosmological constant arises from the
degrees of freedom of the vacuum regarded as a dynamical entity, and a time
variable can be naturally introduced. Taking the scale factor as the sole
degree of freedom of the gravitational field, stationary and wave-packet
solutions to the Wheeler-DeWitt equation are found. It turns out that states of
the Universe with a definite value of the cosmological constant do not exist.
For the wave packets investigated, quantum effects are noticeable only for
small values of the scale factor, a classical regime being attained at
asymptotically large times.Comment: Latex, 19 pages, to appear in Gen. Rel. Gra
Quantum Black Holes from Quantum Collapse
The Schwarzschild black hole can be viewed as the special case of the
marginally bound Lema\^\i tre-Tolman-Bondi models of dust collapse which
corresponds to a constant mass function. We have presented a midi-superspace
quantization of this model for an arbitrary mass-function in a separate
publication. In this communication we show that our solution leads both to
Bekenstein's area spectrum for black holes as well as to the black hole
entropy, which, in this context, is naturally interpreted as the loss of
information of the original matter distribution within the collapsing dust
cloud.Comment: LaTeX file, 6 pages, 1 figure, Paper re-written into sections, some
references added, some elaborations, conclusions unchanged, to appear in
Physical Review
Loop Quantum Gravity: An Inside View
This is a (relatively) non -- technical summary of the status of the quantum
dynamics in Loop Quantum Gravity (LQG). We explain in detail the historical
evolution of the subject and why the results obtained so far are non --
trivial. The present text can be viewed in part as a response to an article by
Nicolai, Peeters and Zamaklar [hep-th/0501114]. We also explain why certain no
go conclusions drawn from a mathematically correct calculation in a recent
paper by Helling et al [hep-th/0409182] are physically incorrect.Comment: 58 pages, no figure