Related papers: The Representation of Numbers in Quantum Mechanics
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
Infinitesimal holomorphic realizations for the Schr\"{o}dinger-Weil representation and the discrete series representations of the Jacobi group are constructed. Explicit expressions of the basic differential operators are obtained. The…
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general dificulty in the formation of human ideas, inherent…
The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe…
Quantum operations arise naturally in many fields of quantum information theory and quantum computing. One of the simplest example of quantum operation is the von Neumann-Lueders measurement. Destruction of states in quantum mechanics can…
By the example of a Fourier transform, the possibilities of Hilbert space geometry applications for statistical model construction are analyzed. In accordance with Bohr's complementarity principle, mutually-complementary coordinate and…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line…
The magnitude of the angular momentum ($J^2$) in quantum mechanics is larger than expected from a classical model. We explain this deviation in terms of quantum fluctuations. A standard quantum mechanical calculation gives the correct…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
In 2007, G.E. Andrews introduced the $(n+1)$-variable combinatorial generating function $R_n(x_1,x_2,\cdots,x_n;q)$ for ranks of $n$-marked Durfee symbols, an $(n+1)$-dimensional multisum, as a vast generalization to the ordinary…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
We show that quantum measures and integrals appear naturally in any $L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$ and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that these operators…
We introduce a formalism that exploits the many-input many-output nature of nodes in quantum circuits. There is a diagrammatic and an algebraic version, the latter similar to the spinor formalism of general relativity. This allows us to…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
We consider a critical composite superconformal string model to desribe hadronic interactions. We present a new approach of introducing hadronic quantum numbers in the scattering amplitudes. The physical states carry the quantum numbers and…