Related papers: Representational conventions and invariant structu…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
The role of impossibilities in theories of Physics is mentioned and a recent result is recalled in which Quantum Mechanics is characterized by three information-theoretic impossibilities. The inconvenience of the asymmetries established by…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of `temporal sequences' of `events' using partial semigroups)…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Reference frames are of special importance in physics. They are usually considered to be idealized entities. However, in most situations, e.g. in laboratories, physical processes are described within reference frames constituted by physical…
Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
In contrast to the intuitively plausible assumption of local realism, entangled particles, even when isolated, are not allowed to possess definite properties in their own right, as quantitatively expressed by violations of Bell's…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
The internal representations learned by deep networks are often sensitive to architecture-specific choices, raising questions about the stability, alignment, and transferability of learned structure across models. In this paper, we…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
The need for revolution in modern physics is a well known and often broached subject, however, the precision and success of current models narrows the possible changes to such a great degree that there appears to be no major change…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
Current theories of particle physics, including the standard model, are dominated by the paradigm that nature is basically translation invariant. Deviations from translation invariance are described by the action of forces. General…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
Light beams can be symmetric under different transformations: translations, rotations, mirror symmetries, duality transformations, etc. In this thesis, a systematic way of characterizing these symmetries is presented. Then, it is shown that…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…