Related papers: Quaternionic Quantum Mechanics: the Particles, the…
Elementary particles are found in two different situations: (i) bound to metastable states of matter, for which angular momentum is quantized, and (ii) free, for which, due to their high energy-momentum and leaving aside inner a.m. or spin,…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum…
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
The existence of a new fundamental scale may lead to modified dispersion relations for particles at high energies. Such modifications seem to be realized with the Planck scale in certain descriptions of quantum gravity. We apply effective…
We review in this paper the use of the theory of scale relativity and fractal space-time as a tool particularly well adapted to the possible development of a future genuine theoretical systems biology. We emphasize in particular the concept…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
In this paper a new approach to investigation of Quantum and Statistical Mechanics of the Early Universe (Planck scale) - density matrix deformation - is proposed. The deformation is understood as an extension of a particular theory by…
A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
Though the Planck scale is encountered in Quantum SuperString Theory and Quantum Gravity, it is the Compton scale of elementary particles which is encountered in the physical world. An explanation for this is given in terms of Brownian…
This is a continuation of a series of papers [FL1, FL2, FL3], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we continue to study the…