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Systems of germs of sets in infinite-dimensional spaces are introduced and studied. Such a system corresponds to a local zero-set of an ideal of the ring of analytic functions of infinite number of variables. Conversely, this system of…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape…
This study looks at motion of particles using mathematical methods of chronometric invariants (physical observable values in General Relativity). It is shown that aside for mass-bearing particles and light-like particles "zero-particles"…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…
An ultraviolet complete particle model is constructed for the observed particles of the standard model. The quantum field theory associates infinite derivative entire functions with propagators and vertices, which make quantum loops finite…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
There appears to be three, perhaps related, ways of approaching the nature of vacuum energy . The first is to say that it is just the lowest energy state of a given, usually quantum, system. The second is to equate vacuum energy with the…
In this letter we address some of the issues raised in the literature about the conflict between a large vacuum energy density, apriori predicted by quantum field theory, and the observed dark energy which must be the energy of vacuum or…
An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and…
We consider systems of n particles that move with constant velocity between collisions. Their total momentum but not necessarily their kinetic energy is preserved at collisions. As there are no further constraints, these systems are…
A "dispersive quantum system" is a quantum system which is both isolated and non-time reversal invariant. This article presents precise definitions for those concepts and also a characterization of dispersive quantum systems within the…
In [1] was considered the superintegrable system which describes the magnetic dipole with spin 1/2 (neutron) in the field of linear current. Here we present its generalization for any spin which preserves superintegrability. The dynamical…
Quantum information refers to the distinctive information-processing properties of quantum systems, which arise when information is stored in or retrieved from nonorthogonal quantum states. More information is required to prepare an…
Vacuum energy in quantum field theory, being the sum of zero-point energies of all field modes, is formally infinite but yet, after regularization or renormalization, can give rise to finite observable effects. One way of understanding how…
Within the framework of quantum electrodynamics (QED), vacuum is a nonlinear medium which can be linearized for a rapidly time-varying electromagnetic field with a small amplitude subjected to a magnetostatic field. The linearized QED…
In a system of n quantum particles, we define a measure of the degree of irreducible n-way correlation, by which we mean the correlation that cannot be accounted for by looking at the states of (n-1) particles. In the case of almost all…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
It is generally assumed that the physical vacuum of particle physics should be characterized by an energy momentum tensor in such a way to preserve exact Lorentz invariance. On the other hand, if the ground state were characterized by its…