Related papers: Natural Theories
We study the mathematical foundations of physics. We reconstruct textbook quantum theory from a single symmetric monoidal functor $GNS : \mathbf{Phys} \longrightarrow \ast\mathbf{Mod}$, based on the Gelfand-Naimark-Segal construction and…
Many of the numbers appearing in the laws of physics, such as the strength of electromagnetism or the masses of elementary particles, must lie in precise ranges for stars, planets, and chemistry to exist. Why the universe has these values…
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…
A modification of the classical primitive equations of the atmosphere is considered in order to take into account important phase transition phenomena due to air saturation and condensation. We provide a mathematical formulation of the…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
This paper argues for the following three theses: (1) There is a clear reason to prefer physical theories with deterministic dynamical equations: such theories are maximally rich in information and usually also maximally simple. (2) There…
We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main…
We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…
We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more…
Naturalness has for many years been a guiding principle in the search for physics beyond the Standard Model, particularly for understanding the physics of electroweak symmetry breaking. However, the discovery of the Higgs particle at 125…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
We develop a monadic framework formalising an operational notion of dynamics, seen as the setting and evolution of initial value problems, in general physical theories. We identify in the Eilenberg-Moore category the natural environment for…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
The existing field theories are based on the properties of closed exterior forms, which correspond to conservation laws for physical fields. In the present paper it is shown that closed exterior forms corresponding to field theories are…
Some elements of classical mechanics and classical statistical mechanics are formulated in terms of fibre bundles. In the bundle approach the dynamical and distribution functions are replaced by liftings of paths in a suitably chosen…
The Standard Model of elementary particles is a theory unifying three of the four basic forces of the Nature: electromagnetic, weak, and strong interactions. In this paper we consider the Standard Model in the presence of a classical…
One of the main activities in science teaching, and in particular in Physics teaching, is not only the discussion of both modern problems and problems which solution is an urgent matter. It means that the picture of an active and alive…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
This series of lectures is planned as a generalization of author's large (more than fifteen years) experience of work in the theoretical physics. The modern theoretical physics is based on the group-theoretical approach which generates the…
The theory of natural selection has two forms. Deductive theory describes how populations change over time. One starts with an initial population and some rules for change. From those assumptions, one calculates the future state of the…