Related papers: Dynamic and Geometric Phase Formulasin the Hestene…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar \omega$ in each mode, i.e., the zero-point Planck spectrum. While this…
Several definitions of phase have been proposed for stochastic oscillators, among which the mean-return-time phase and the stochastic asymptotic phase have drawn particular attention. Quantitative comparisons between these two definitions…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wavefunction and a recently proposed quantum hydrodynamical description of its dynamics. An…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
We study the structure of the phase space of generic models of deformed special relativity that gives rise to a definition of velocity consistent with the deformed Lorentz symmetry. As a byproduct we also determine the laws of…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…