Related papers: Properties of a Two-Sphere Singularity
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as…
The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electro-magnetic field, calculate their…
The groundstate configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as function of the inter-atomic distance (d). The classical particles are confined by identical harmonic wells and repel each…
Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…
Electromagnetic properties of quark-like particles are examined in a classical field model involving extended dual electromagnetic fields. These can have fractional charges and a confining potential that derives essentially completely from…
Anomalies can be anticipated at the classical level without changing the classical cohomology, by introducing extra degrees of freedom. In the process, the anomaly does not quite disappear. We show that, in fact, it is shifted to new…
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…
We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In a duality family, once a system is solved, all other…
The classical and quantum properties of a new solution obtained in $2+1$% -dimensional gravity coupled with a real scalar field is analyzed in detail. The considered new solution is a one-parameter generalization of a previously known…
We analyze the persistence of curvature singularities when analyzed using quantum theory. First, quantum test particles obeying the Klein-Gordon and Chandrasekhar-Dirac equation are used to probe the classical timelike naked singularity. We…
After reviewing the definitions of classical and quantum singularities, it is shown by example that if zeroth-order curvature invariants are regular, a diverging higher-order curvature invariant does not necessarily imply the existence of a…
Permutations of particle labels are usually used to illustrate the relationship between classical and quantum statistics. We use permutations of attributes/properties of particles to express properties of waves. We express events of the…
We study properties of non-minimal biharmonic hypersurfaces of spheres. The main result is a CMC Unique Continuation Theorem for biharmonic hypersurfaces of spheres. We then deduce new rigidity theorems to support the Conjecture that…
The quantum theory of a spatially flat Friedmann-Robertson-Walker universe with a massless scalar field as source is further investigated. The classical model is singular, and in the framework of the Arnowitt-Deser-Misner canonical…
We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain…
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…