Related papers: Linking the Foundations of Physics and Mathematics
In this article we consider alternative definitions-descriptions of a set being Infinite within the primitive Axiomatic System of Zermelo.
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the…
The simple examples of spontaneous breaking of various symmetries for the scalar theory with fundamental mass have been considered. Higgs generalizations on "fundamental mass" were introduced into the theory on a basis of the…
Concept of inertial mass is not well defined in physics. For defining inertial mass of a particle we need to know its acceleration under some force in an inertial reference frame, which itself is defined by the motion of its background…
Canonical coordinates for the Schr\"odinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schr\"odinger equation, considered as a classical field theory, shares with Liouville completely…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
The canonical quantum theory of a free field using arbitrary foliations of a flat two-dimensional spacetime is investigated. It is shown that dynamical evolution along arbitrary spacelike foliations is unitarily implemented on the same Fock…
I describe an approach which relates classical gravity to the quantum microstructure of spacetime. In this approach, the field equations arise from maximizing the density of states of the matter plus geometry. The former is identified using…
The generalized Schrodinger equation deduced in the earlier papers is compared with conventional constructions of quantum field theory. In particular, it yields the usual Schrodinger equation of quantum field theory written without normal…
It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame a quantum field theory, or a thermodynamic system with…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
The concept of the elegant work introduced by Levai in Ref. [5] is extended for the solutions of the Schrodinger equation with more realistic other potentials used in different disciplines of physics. The connection between the present…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by…
Any time-dependent solution of Schr\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to…
In this article we will discuss a few aspects of the spacetime description of matter and fields. In Section:1 we will discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric…
We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate peturbatively the law of addition of momenta…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…