Related papers: Quaternionic Taub-NUT from the harmonic space appr…
The presence of a cosmological constant, Lambda, in an action with higher powers of the curvature can produce rapidly oscillating metrics. We develop a perturbative approach for generating periodic solutions to the non-linear field…
The occurrence of chaos for test particles moving in a Taub-NUT spacetime with a dipolar halo perturbation is studied using Poincar\'e sections. We find that the NUT parameter (magnetic mass) attenuates the presence of chaos.
A path-integral method effective beyond the perturbation expansion approach is suggested to consider the quartic anharmonicity in different spatial dimensions. Due to an optimal representation of the partition function, the leading term has…
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented.…
Wheeler's approach to finding exact solutions in Lovelock gravity has been predominantly applied to static spacetimes. This has led to a Birkhoff's theorem for arbitrary base manifolds in dimensions higher than four. In this work, we…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperK\"ahler with Torsion). The…
It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity…
For $U(2)$-invariant 4-metrics, we show that the $B^t$-flat metrics are very different from the other canonical metrics (Bach-flat, Einstein, extremal K\"ahler, etc). We show every $U(2)$-invariant metric is conformal to two separate…
The classical Hamilton equations are reinterpreted by means of complex analysis, in a non standard way. This suggests a natural extension of the Hamilton equations to the quaternionic case, extension which coincides with the one introduced…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying…
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
We construct an asymptotic metric on the moduli space of two centred hyperbolic monopoles by working in the point particle approximation, that is treating well-separated monopoles as point particles with an electric, magnetic and scalar…
We show that in an asymptotically flat space where an S-Matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct super-selection sectors,…
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…
We consider a class of axially symmetric solutions to Einstein's equations incorporating a $\theta$-dependent scalar field and extend these solutions by introducing electric and magnetic charges via Harrison transformations. Subsequently,…
We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a…
It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass ($M = m$), the "angular…
Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…