Related papers: Observables and a Hilbert Space for Bianchi IX
We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert Space followed by an imposition of - what effectively amounts to - a superselection rule. We illustrate this procedure with a qubit and apply it to…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
We explore the dynamical stability of the minisuperspace Hamiltonian of the Bianchi IX cosmological models, giving a gauge-invariant and unapproximated description of the full continuous dynamics, achieved through a geometrical description…
We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency…
We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analysis is mainly based on numerical simulations. The properties…
In topological equivalence, a bounded linear operator between Banach spaces - we focus on the case of Hilbert spaces - is viewed as only acting linearly and continuously between them qua different spaces with the structure of linear…
We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver.…
The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing…
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space $\left(x,k\right)$ into Hilbertian operators. The…
The quantization of Class A Bianchi Type VI and VII geometries -with all six scale factors, as well as the lapse function and the shift vector present- is considered. A first reduction of the initial 6-dimensional configuration space is…
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they…
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…
Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…
We argue that Hilbert spaces are not suitable to represent quantum states mathematically, in the sense that they require properties that are untenable by physical entities. We first demonstrate that the requirements posited by complex inner…
In this paper, we will generelize $b$-frames; a new concept of frames for Hilbert spaces, by $K$-$b$-frames. The idea is to take a sequence from a Banach space and see how it can be a frame for a Hilbert space. Instead of the scalar product…
Quantum states of the diagonal Bianchi type IX model with negative cosmological constant $\Lambda$ are obtained by transforming the Chern-Simons solution in Ashtekar's variables to the metric representation. We apply our method developed…