40 citations · 396 across the 36 of their papers we have counts for
36 papers
Differential geometry using quaternions
Sergio Giardino
This paper establishes the basis of the quaternionic differential geometry ($\mathbbm H$DG) initiated in a previous article. The usual concepts of curves and surfaces are generaliz…
Spin and angular momentum in quaternionic quantum mechanics
Sergio Giardino
We present two novel solutions of real Hilbert state quaternionic quantum mechanics (QM). Firstly, we observe that the angular momentum operator admits two different cla…
Quaternionic fermionic field
Sergio Giardino
The second quantization of the quaternionic fermionic field is undertaken using the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The solution res…
Attenuated gravitational radiation
Sergio Giardino
The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation…
Quaternionic scalar field in the real Hilbert space
Sergio Giardino
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as w…
Winding number and homotopy for quaternionic curves
Sergio Giardino
Following a recent approach to quaternionic curves, we defined the quaternionic polar angle that enabled us to define global properties of quaternionic curves, namely the winding n…
Quaternionic Dirac free particle
Sergio Giardino
We solve the quaternionic Dirac equation ($\mathbbm H$DE) in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of…
A complementary covariant approach to gravito-electromagnetism
Sergio Giardino
From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in…
A primer on the differential geometry of quaternionic curves
Sergio Giardino
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic cu…
Quaternionic Klein-Gordon equation
Sergio Giardino
We solve Klein-Gordon equation (KGE) in the framework of the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The presented solution is the simplest…
Quaternionic quantum harmonic oscillator
Sergio Giardino
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the…
Quaternionic elastic scattering
Sergio Giardino
We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive expression for the wave fu…
Quaternionic electrodynamics
Sergio Giardino
We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the ele…
Square-well potential in quaternic quantum mechanics
Sergio Giardino
The one-dimensional infinite square well is the simplest solution of quantum mechanics, and consequently one of the most important. In this article, we provide this solution using…
Virial theorem and generalized momentum in quaternic quantum mechanics
Sergio Giardino
After a review on recent results on quaternic quantum mechanics (QM), we present further consistency tests that reinforce its compatibility with the usual complex quant…
A novel covariant approach to gravito-electromagnetism
Sergio Giardino
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two aux…
Quaternionic quantum mechanics in real Hilbert space
Sergio Giardino
A formulation of quaternionic quantum mechanics (QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral t…
Quaternionic quantum particles: new solutions
Sergio Giardino
If is a quaternionic wave function, then . Thus, there are two versions of the quaternionic Schrödinger equation (QSE). In this article, we present the second possib…
Quaternionic quantum particles
Sergio Giardino
Solutions of quaternionic quantum mechanics (QQM) are difficult to grasp, even in simple physical situations. In this article, we provide simple and understandable free particle qu…
Non-anti-hermitian quaternionic quantum mechanics
Sergio Giardino
The breakdown of Ehrenfest's theorem imposes serious limitations on quaternionic quantum mechanics (QQM). In order to determine the conditions in which the theorem is valid, we exa…
Quaternionic Aharonov-Bohm effect
Sergio Giardino
A quaternionic analog of the Aharonov-Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics (QQM). A quaternionic phase links the so…
Four-dimensional conformal field theory using quaternions
Sergio Giardino
We build a four-dimensional quaternion-parametrized conformal field theory (QCFT) using quaternion holomorphic functions as the generators of quaternionic conformal transformations…
Tunnelling of Pulsating Strings in Deformed Minkowski Spacetime
Sergio Giardino, Victor Rivelles
Using the WKB approximation we analyse the tunnelling of a pulsating string in deformed Minkowski spacetime.
Möbius transformation for left-derivative quaternion holomorphic functions
Sergio Giardino
Holomorphic quaternion functions only admit affine functions; thus, the Möbius transformation for these functions, which we call quaternionic holomorphic transformation (QHT), only…