Related papers: Thoughts on Commutation Relations and Measurement …
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
We have studied the different symmetric properties of the generalized Maxwell's - Dirac equation along with their quantum properties. Applying the parity (\mathcal{P}), time reversal (\mathcal{T}), charge conjugation (\mathcal{C}) and their…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the…
The ability to control electronic states at the nanoscale has contributed to our modern understanding of condensed matter. In particular, quantum dot circuits represent model systems for the study of strong electronic correlations,…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…
This paper presents a comprehensive review of the wave-function approach for derivation of the number-resolved Master equations, used for description of transport and measurement in mesoscopic systems. The review contains important…
A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be…
We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module of derivations into free modules; [2] the existence of a…
Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding…
We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position…
It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz…
Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to…
The electromagnetic-vacuum-field fluctuations are intimately linked to the process of spontaneous emission of light. Atomic emitters cannot probe electric- and magnetic-field fluctuations simultaneously because electric and magnetic…
We study a single quantum particle in discrete spacetime evolving in a causal way. We see that in the continuum limit any massless particle with a two dimensional internal degree of freedom obeys the Weyl equation, provided that we perform…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…
It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit…
One can construct the model conception of quantum phenomena (MCQP) which relates to the axiomatic conception of quantum phenomena (ACQP), (i.e. to the conventional quantum mechanics) in the same way, as the statistical physics relates to…
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…