Related papers: Towards an octonionic world
Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing…
The matrix elements connected non physic angles space representation with the space of physic observables of alternative O(2,4) world found on explicit form. All such matrix elements are represented in terms of solutions of Gauss…
We use the theory of functions of noncommuting operators (noncommutative analysis) to solve an asymptotic problem for a partial differential equation and show how, starting from general constructions and operator formulas that seem to be…
Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling…
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 responds to an open problem of quaternionic quantum theory, and…
Courses on undergraduate quantum mechanics usually focus on solutions of the Schr\"odinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced only academic examples are used, such as the…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
We study the quantum mechanics of BMN operators with two scalar impurities and arbitrarily many traces, at one loop and all genus. We prove an operator identity which partially elucidates the structure of this quantum mechanics, provides…
Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to…
We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary operator which…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
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…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
We combine the ideas of Dirac's orthonormal representation, Everett's relative state, and 't Hooft's ontological basis to define the notion of a world for quantum mechanics. Mathematically, for a quantum system $\mathcal{Q}$ with an…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…