scholarly journals Symmetries in Foundation of Quantum Theory and Mathematics

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 409 ◽  
Author(s):  
Felix M. Lev
Keyword(s):  
Quantum Theory ◽  
Dark Energy ◽  
Lie Algebra ◽  
De Sitter ◽  
Classical Level ◽  
Standard Quantum ◽  
Background Space ◽  
Classical Mathematics ◽  
Formal Limit ◽  
And Mathematics

In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite—background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare symmetry can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario in which the phenomenon of cosmological acceleration can be explained by proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic p and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

scholarly journals What If Quantum Theory Violates All Mathematics?

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 598-602
Author(s):  
Elemér Elad Rosinger
Keyword(s):  
Mathematical Logic ◽  
Quantum Theory ◽  
Bell Inequalities ◽  
List Type ◽  
Elementary Argument ◽  
And Mathematics

Abstract It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on … An interest in that result is due to the following three alternatives which it imposes upon both Physics and Mathematics: Quantum Theory is inconsistent. Quantum Theory together with Mathematics are inconsistent. Mathematics is inconsistent. In this regard one should recall that, up until now, it is not known whether Mathematics is indeed consistent.

scholarly journals QUANTUM INTEGRABILITY OF COUPLED N=1 SUPER SINE/SINH–GORDON THEORIES AND THE LIE SUPERALGEBRA D(2,1;α)

1999 ◽  
Vol 14 (16) ◽  
pp. 2551-2580 ◽  
Author(s):  
JONATHAN M. EVANS ◽  
JENS OLE MADSEN
Keyword(s):  
Quantum Theory ◽  
Lie Superalgebra ◽  
Field Theories ◽  
Continuous Family ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Classical Level ◽  
Quantum Integrability ◽  
Integrable Quantum ◽  
Conserved Currents

We discuss certain integrable quantum field theories in 1+1 dimensions consisting of coupled sine/sinh–Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that theories of this type can be constructed as Toda models based on the exceptional affine Lie superalgebra D(2,1;α)(1) (or on related algebras which can be obtained as various limits) provided one adopts appropriate reality conditions for the fields. In particular, there is a continuous family of such models in which the couplings and mass ratios all depend on the parameter α. The structure of these models is analyzed in some detail at the classical level, including the construction of conserved currents with spins up to 4. We then show that these currents generalize to the quantum theory, thus demonstrating quantum-integrability of the models.

scholarly journals Fine Structure of Dark Energy and New Physics

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Vishnu Jejjala ◽  
Michael Kavic ◽  
Djordje Minic
Keyword(s):  
Fine Structure ◽  
Quantum Theory ◽  
Dark Energy ◽  
Cosmological Constant ◽  
New Physics ◽  
Blackbody Radiation ◽  
Cosmological Constant Problem ◽  
Radiation Problem ◽  
Specific Proposal ◽  
Dual Quantum

Following our recent work on the cosmological constant problem, in this letter we make a specific proposal regarding the fine structure (i.e., the spectrum) of dark energy. The proposal is motivated by a deep analogy between the blackbody radiation problem, which led to the development of quantum theory, and the cosmological constant problem, for which we have recently argued calls for a conceptual extension of the quantum theory. We argue that the fine structure of dark energy is governed by a Wien distribution, indicating its dual quantum and classical nature. We discuss observational consequences of such a picture of dark energy and constrain the distribution function.

RICCION AS A COSMIC DARK MATTER CANDIDATE AND LATE COSMIC ACCELERATION

2008 ◽  
Vol 23 (31) ◽  
pp. 2681-2689
Author(s):  
S. K. SRIVASTAVA ◽  
K. P. SINHA
Keyword(s):  
Energy Source ◽  
Dark Matter ◽  
Dark Energy ◽  
Cosmic Acceleration ◽  
Exotic Matter ◽  
Dark Matter Candidate ◽  
Classical Level ◽  
The Past ◽  
Higher Derivative

In the past few years, a possibility is investigated, where curvature itself behaves as a source of dark energy. So, it is natural to think whether curvature can produce dark matter too. It is found that, at classical level, higher-derivative gravity yields curvature inspired particles namely riccions.31 Here, it is probed whether riccion can be a possible source of dark matter. Further, it is found that the late universe accelerates. Here, it is interesting to see that acceleration is obtained from curvature without using any dark energy source of exotic matter.

Fuzzy Set Theory Applied to Accounting Sciences

2020 ◽  
Vol 16 (01) ◽  
pp. 1-16
Author(s):  
Carmen Lozano ◽  
Enriqueta Mancilla-Rendón
Keyword(s):  
Social Sciences ◽  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Hamming Distance ◽  
Great Acceptance ◽  
Classical Mathematics ◽  
Triangular Numbers ◽  
And Mathematics

Fuzzy set theory and fuzzy logic have been successfully developed in engineering and mathematics. However, these concepts have found great acceptance in social sciences in recent years since they provide an answer to those problems in the real world that cannot be modeled using classical mathematics. In this paper, we propose a new methodology for accounting science based on fuzzy triangular numbers. The methodology uses Hamming distance between fuzzy triangular numbers and arithmetic operations to evaluate corporate governance of multinational public stock corporations (PSCs) in the telecommunications sector.

Dynamical system approach for the modified Brans–Dicke theory

2019 ◽  
Vol 28 (10) ◽  
pp. 1950132 ◽  
Author(s):  
Jianbo Lu ◽  
Xin Zhao ◽  
Shining Yang ◽  
Jiachun Li ◽  
Molin Liu
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
Critical Point ◽  
System Approach ◽  
State Parameter ◽  
Kinetic Term ◽  
De Sitter ◽  
Dynamical System Approach ◽  
De Sitter Universe ◽  
Manifold Theory

A modified Brans–Dicke theory (abbreviated as GBD) is proposed by generalizing the Ricci scalar [Formula: see text] to an arbitrary function [Formula: see text] in the original BD action. It can be found that the GBD theory has some interesting properties, such as solving the problem of PPN value without introducing the so-called chameleon mechanism (comparing with the [Formula: see text] modified gravity), making the state parameter to crossover the phantom boundary: [Formula: see text] without introducing the negative kinetic term (comparing with the quintom model). In the GBD theory, the gravitational field equation and the cosmological evolutional equations have been derived. In the framework of cosmology, we apply the dynamical system approach to investigate the stability of the GBD model. A five-variable cosmological dynamical system and three critical points ([Formula: see text], [Formula: see text], [Formula: see text]) are obtained in the GBD model. After calculation, it is shown that the critical point [Formula: see text] corresponds to the radiation dominated universe and it is unstable. The critical point [Formula: see text] is unstable, which corresponds to the geometrical dark energy dominated universe. While for case of [Formula: see text], according to the center manifold theory, this critical point is stable, and it corresponds to geometrical dark energy dominated de Sitter universe ([Formula: see text]).

scholarly journals Holographic dark energy model in unimodular f(T) gravity

2019 ◽  
Vol 16 (01) ◽  
pp. 1950003
Author(s):  
A. E. Godonou ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Teleparallel Gravity ◽  
De Sitter ◽  
Holographic Dark Energy Model ◽  
Reconstruction Procedure ◽  
Perfect Agreement ◽  
Text Data ◽  
Viable Model ◽  
Reconstructed Model

This work deals with holographic dark energy in the context of unimodular [Formula: see text] gravity, which is a modification of teleparallel gravity. We develop the general reconstruction procedure of the [Formula: see text] form that can yield the holographic feature of the dark energy. We fit the reconstructed model with the [Formula: see text] data and our results show a perfect agreement with the WMAP9 cosmological observational data, at least for the range [Formula: see text]. We investigate the consistency of the reconstructed model by studying its stability against linear gravitational and matter perturbations, fixing [Formula: see text] to [Formula: see text]. The model presents stability for both de Sitter and power-law solutions and we conclude that it is a good candidate as alternative viable model for characterizing holographic dark energy.

scholarly journals MODIFIED GRAVITATIONAL THEORIES AND COSMIC ACCELERATION

2004 ◽  
Vol 19 (31) ◽  
pp. 5343-5350 ◽  
Author(s):  
DAMIEN A. EASSON
Keyword(s):  
Dark Energy ◽  
Cosmic Acceleration ◽  
Late Time ◽  
De Sitter ◽  
Gravitational Theories ◽  
Hilbert Action

Modified gravitational theories can provide alternatives to dark energy as an explaination for the observed late-time cosmic acceleration. Several examples of low-curvature corrections to the Einstein-Hilbert action are studied. These models generically contain unstable de Sitter solutions and, depending on the parameters of the theory, can exhibit late time accelerating attractor solutions.

scholarly journals de Sitter duality and logarithmic decay of dark energy

2020 ◽  
Vol 101 (2) ◽  
Author(s):  
Hiroyuki Kitamoto ◽  
Yoshihisa Kitazawa ◽  
Takahiko Matsubara
Keyword(s):  
Dark Energy ◽  
De Sitter ◽  
Logarithmic Decay

scholarly journals Local Realistic Theory for PDC Experiments Based on the Wigner Formalism

2001 ◽  
Vol 56 (1-2) ◽  
pp. 178-181 ◽  
Author(s):  
Alberto Casado ◽  
Ramón Risco-Delgado ◽  
Emilio Santos
Keyword(s):  
Quantum Theory ◽  
Radiation Field ◽  
Hidden Variables ◽  
Standard Quantum ◽  
Realistic Theory ◽  
Photon Pairs ◽  
Parametric Down Conversion ◽  
Wigner Representation ◽  
Down Conversion ◽  
Made In

Abstract In this article we present a local hidden variables model for all experiments involving photon pairs produced in parametric down conversion, based on the Wigner representation of the radiation field. A modification of the standard quantum theory of detection is made in order to give a local realistic explanation of the counting rates in photodetectors. This model involves the existence of a real zeropoint field, such that the vacumm level of radiation lies below the threshold of the detectors.

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