Related papers: Quaternionic Wavefunction
The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using…
We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…
We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are…
This manuscript presents an attempt to introduce Lagrangian formalism for mechanical systems using para-quaternionic Kahler manifolds, which represent an interesting multidisciplinary field of research. In addition to, the…
This paper systematically develops the Schr\"odinger formalism that is valid also for gyrotropic media where the material weights $W = \left ( \begin{smallmatrix} \varepsilon & \chi \chi^* & \mu \end{smallmatrix} \right ) \neq \overline{W}$…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The…
We propose that the four-velocity of a Dirac particle is related to its relativistic wave function by $u^i=\bar{\psi}\gamma^i\psi/\bar{\psi}\psi$. This relativistic wave$-$particle duality relation is demonstrated for a free particle…
We extract the square root of the Minkowski metric using Dirac/Clifford matrices. The resulting $4\times 4$ operator $d{\bf S}$ that represents the square root, can be used to transform four vectors between relatively moving observers. This…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
Phenomenological potentials describe the quarkonium systems like Charmonia, Bottomonia and $B_c$ Meson. They give a good accuracy for the mass spectra. In the present work we extend one of our previous works in the central case by adding…
Starting from first principles and general assumptions based on the energy-momentum relation of the Special Theory of Relativity we present a novel wave equation for ultrarelativistic matter. This wave equation arises when particles satisfy…
In this article we use an electromagnetic Lagrangian constructed so as to include dispersive effects in the description of an electromagnetic wave propagating in the Quantum Electrodynamic Vacuum. This Lagrangian is Lorentz invariant,…
New solutions of relativistic wave equations are obtained in a unified manner from generating functions of spinorial variables. The choice of generating functions as Gaussians leads to representations in the form of generalized fractional…
We present the complete first order relativistic quantum kinetic theory with spin for massive fermions derived from the Wigner function formalism in a concise form that shows explicitly how the 32 Wigner equations reduce to 4 independent…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
A relativistic version of the correspondence principle, a limit in which classical electrodynamics may be derived from QED, has never been clear, especially when including gravitational mass. Here we introduce a novel classical field theory…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of…