Related papers: Bringing Up a Quantum Baby
We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundamental techniques from the theory of order unit spaces and…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
We consider the characteristic time operator $\mathsf{T}$ introduced in [E. A. Galapon, Proc. R. Soc. Lond. A, 458:2671 (2002)] which is bounded and self-adjoint. For a semibounded discrete Hamiltonian $\mathsf{H}$ with some growth…
We construct a category $\mathrm{HomCob}$ whose objects are {\it homotopically 1-finitely generated} topological spaces, and whose morphisms are {\it cofibrant cospans}. Given a manifold submanifold pair $(M,A)$, we prove that there exists…
It is now well established that quantum tomography provides an alternative picture of quantum mechanics. It is common to introduce tomographic concepts starting with the Schrodinger-Dirac picture of quantum mechanics on Hilbert spaces. In…
We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by…
We investigate the classical aspects of Quantum theory and under which description Quantum theory does appear Classical. Although such descriptions or variables are known as "ontological" or "hidden", they are not hidden at all, but are…
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in "natural form",…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of…