The flat FRW model in LQC: self-adjointness
نویسندگان
چکیده
منابع مشابه
ar X iv : 0 70 9 . 31 20 v 1 [ gr - q c ] 1 9 Se p 20 07 The flat FRW model in LQC : the self - adjointness
The flat FRW model coupled to the massless scalar field according to the improved, background scale independent version of Ashtekar, Pawlowski and Singh [1] is considered. The core of the theory is addressed directly: the APS construction of the quantum Hamiltonian is analyzed under the assumption that cosmological constant Λ ≤ 0. We prove the essential self-adjointness of the operator whose sq...
متن کاملDynamical properties of the conformally coupled flat FRW model
In this paper we study the dynamical behaviour of a simple cosmological model defined by a spatially flat Robertson-Walker geometry, conformally coupled with a massive scalar field. We determine a Lyapunov-like function for the non-linear evolution equations. From this function we prove that all the stationary solutions are unstable. We also show that all initial conditions, different from the ...
متن کاملEssential self - adjointness
1. Cautionary example 2. Criterion for essential self-adjointness 3. Examples of essentially self-adjoint operators 4. Appendix: Friedrichs' canonical self-adjoint extensions 5. The following has been well understood for 70-120 years, or longer, naturally not in contemporary terminology. The differential operator T = d 2 dx 2 on L 2 [a, b] or L 2 (R) is a prototypical natural unbounded operator...
متن کاملGauge-invariant perturbations in a flat FRW universe.
Starting out with new deenitions for the gauge-invariant perturbations in energy density and particle number density, evolution equations for these quantities are derived which are manifestly gauge-invariant. In the case of vanishing pressure, these equations are identical to Poisson's equation. This fact is in contrast to what is found in earlier treatments based on other dee-nitions.
متن کاملContinuation semantics and self-adjointness
We give an abstract categorical presentation of continuation semantics by taking the continuation type constructor : (or cont in Standard ML of New Jersey) as primitive. This constructor on types extends to a contravariant functor on terms which is adjoint to itself on the left; restricted to the subcategory of those programs that do not manipulate the current continuation, it is adjoint to its...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Classical and Quantum Gravity
سال: 2008
ISSN: 0264-9381,1361-6382
DOI: 10.1088/0264-9381/25/3/035001