Related papers: Towards an octonionic world
We present a matrix formalism, inspired by the Minkowski four-vectors of special relativity, useful to solve classical physics problems related to both mechanics and thermodynamics. The formalism turns out to be convenient to deal with…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with Darboux method are used to obtain the bound states energy…
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac…
We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
In a 1+1 dimensional model of plane gravitational waves the flux-holonomy algebra of loop quantum gravity is modified in such a way that the new basic operators satisfy canonical commutation relations. Thanks to this construction it is…
Dirac's operator and Maxwell's equations in vacuum are derived in the algebra of split octonions. The approximations are given which lead to classical Maxwell-Heaviside equations from full octonionic equations. The non-existence of magnetic…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…