Related papers: Directional Quantum Singularities in Curzon Spacet…
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equation becomes singular in the sense that…
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…
A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QW admit, as their continuum limit, a well-known equation of Physics. In arXiv:1803.01015 the QW is…
One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic ideas of the BKL picture suggest that oscillatory singularities…
A nonsingular localized static classical solution is constructed for standard Einstein gravity coupled to an $SO(3)\times SO(3)$ chiral model of scalars (Skyrme model). This solution corresponds to a spacetime defect and its construction…
Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated in SI93, we identify two classes of peculiar interest: focusing timelike singularity…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.
Chiral boson fields in (1+1) dimensions obey a first order equation of motion. A second order equation which classically describes two chiral boson fields of the same chirality leads, however, to an unacceptable quantum theory
A class of noncanonical effective potentials is introduced allowing stable, radially symmetric, solutions to first order Bogomol'nyi equations for a real scalar field in a fixed spacetime background. This class of effective potentials…
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). In this paper, we study the…
The standard setting of quantum computation for continuous problems uses deterministic queries and the only source of randomness for quantum algorithms is through measurement. This setting is related to the worst case setting on a classical…
We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular…
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…
This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in $D$-dimensional spacetime. These solutions are found by…
We quantize the Schwarzschild spacetime with naked singularity using the affine coherent states quantization method. The novelty of our approach is quantization of both temporal and spatial coordinates. Quantization smears the gravitational…
The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…
For a massive scalar field in a fixed Schwarzschild background, the radial wave equation obeyed by Fourier modes is first studied. After reducing such a radial wave equation to its normal form, we first study approximate solutions in the…
Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by…
We model a single-electron ion (hydrogenic atom) as a static, spherically symmetric electrovacuum spacetime in which the nucleus is treated as a timelike line-singularity and the electron is treated as a test particle following Dirac's…