Symmetry in Geometrical Physics

Dear Colleagues,

In recent years, rapid developments have taken place in nonlocal-in-time theories characterized by the occurrence of higher-order derivatives. Time non-locality arises in a large number of physical phenomena including classical mechanics, dissipative dynamics, the self-diffusion process, geometrical physics, discrete quantum mechanics, quantum field theory, and the theory of parabolic and hyperbolic differential equations, among others. Nevertheless, after a large number of theoretical studies, it was observed that higher-order derivatives hold a number of generic outcomes, and they constitute an indispensable mathematical tool nowadays in theoretical physics and sciences, e.g., in Abraham–Lorentz electrodynamics theory, which describes the equation of motion for charged particles taking into account radiative effects. There are quite a lot of methodologies that deal with higher-order derivative theories, e.g., the method of perturbative constraints, which is used to study dynamical systems characterized by equations of motion depending on more than one moment in time, in addition to the backward and forward shifting coordinates/positions in time and the nonlocal-in-time kinetic energy approach. These theoretical methodologies were used in quantum mechanics, in stochastic dynamics, and in fluid dynamics, etc. The main aim of this Special Issue is to enlarge the domain of applications of nonlocal-in-time approaches, mainly the nonlocal-in-time kinetic energy approach in different fields in particular classical and quantum mechanics, quantum hydrodynamics, kinetic theory, solid state physics, classical and quantum electrodynamics, and relativity theory, among others.

Prof. Rami Ahmad El-Nabulsi
Guest Editor

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• nonlocal-in-time kinetic energy
• quantum physics
• quantum hydrodynamics
• kinetic theory in statistical physics
• solid-state physics
• electrodynamics
• nonlocal geometrodynamics
• relativity theory (special and general)