Related papers: Hyper-atoms applied to the critical pair Theory
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present…
The Riemann hypothesis is proved by quantum-extending the zeta Riemann function to a quantum mapping between quantum $1$-spheres with quantum algebra $A=\mathbb{C}$, in the sense of A. Pr\'astaro \cite{PRAS01, PRAS02}. Algebraic topologic…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly…
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
We introduce a quantum generalisation of the notion of coupling in probability theory. Several interesting examples and basic properties of quantum couplings are presented. In particular, we prove a quantum extension of Strassen theorem for…
Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results and it is…
Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr's coordination-causality complementarity…
A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…
We consider a hypothetical substance, where interaction between (within) structural elements of condensed matter (molecules, nanoparticles, clusters, layers, wires etc.) depends on state of Cooper pairs: an additional work must be made…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…
The axioms of quantum mechanics provide limited information regarding the structure of the Hilbert space, such as the underlying number system. The latter is generally regarded as complex, but generalizations of complex numbers, so-called…
Effective theories based on experimental data provide powerful probes and tests of underlying theories in elementary particle physics. Examples within and beyond the Standard Model are discussed, including a specific model for supersymmetry…
We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equivalent to measurability, but it is well-known that choice is…
The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have…